MF is probably the only Marksman champ that can realistically choose Hybrid, full AD, or full AP to her liking and be effective regardless. Ezreal as AP can't wave clear, and is purely burst with no sustained damage whatsoever; As Hybrid Ezreal just has a sub-par Q, Sub-par W, Sub-par E, and Mediocre Ult.
Meanwhile MF has the crazy 80% scaling on her E for AP, 35% scaling with Q and 50% scaling on the bounce, and the Ult has 20% scaling on her ult for AP that is translated into Physical damage. So long as you build enough penetration, she'll be fine because with these items she's prepared for any situation. She's the dankest backline artillery, especially when you have AP, and has excellent mobility with W and ghost in team fights to run away from backline divers like Olaf and Kennen, and in lane, bullies many champs by simply building in an order to their counter.
I like Full AP MF, but Hybrid is more effective IMO because she'll have all of her attacks (Auto, q, E, R) be effective in battle with this build. AP might scale on her ult and Q to add damage (20% ult 35%/50% Q) but since it's translated into physical damage you still need Physical penetration.

You may easily swap out Hybrid Pen for Magic Penetration. Since you build Mortal reminder, Magic penetration becomes more valuable.
If you want to swap the CDR runes for AP runes that's fine just remember to get your full 40% CDR through Lucidity boot or some other item with 10% CDR.
Armor yellows can be used instead of Health regen or Health flats if you're fighting an assassin, but Health is the most well rounded. The Yellows can be honestly anything to your preference.
On the reds, I actually prefer to run Armor red. Against a heavy AD team I might still go with both scaling armor yellows and the armor reds, but most often I run Armor reds with Flat health runes. However I know people prefer the hybrid penetration runes because they're okay with being a super squishy carry. I'm not.

I run Deathfire touch instead of thunderlord's because it scales harder than Thunderlord's.
Deathfire's is 8 damage plus 60% of your AD and 25% of your AP, while Thunder's is 10 Per level and 30% AD with 10% AP.
At early levels, like level 3 or 6, Thunder's deals significantly more damage, but scales a LOT less of your stats for later in the game, and this entire build was not designed for winning the early, it's for coming back from a lost lane or pressing hard on a won lane. So instead of compensating for it with a weak scaling. THE GAME IS NOT ALWAYS ABOUT WINNING YOUR LANE. If you're easily tilted do NOT use this build, a lost lane might happen, you have to believe in scaling.
Also, while it may be good to proc Thunder's on your E or Ult easy, Deathfire stacks with Liandry's torment allowing you to pick off escaping enemies, especially since Liandry's deals CURRENT HEALTH, so it can't last hit an enemy at all.
I like expose weakness because of the "Believe in the scaling" idea. You may choose to run feast for good sustain for a better laning phase, which is perfectly acceptable. You may be a bit more solo-oriented so you like to run double edge sword. I main support so I'm good at synergizing with teams so I wrap my playstyle around that.
You can choose to run Battering Blows instead of Peircing thoughts, or even run a few points of either. Choosing Battering blows scales on 3 attacks while Piercing thoughts is only for your E, so you may like to capitalize on Physical penetration. However, since there IS no percent piercing on AP, I like to run that mastery so help with the low AP values you might get to ensure your E is more effective. Against tanks that 7% is actually QUITE a bit, and more valuable than the limited Magic pen you can get. You can only get your 15 from Sorc boots and 15 from Liandry's, so if someone stacks 150+ MR that 7% turns out to be quite a bit of penetration, 10.7 Pen if they have 150.

You gotta use your brain. There are 4 core items that combined allow you to handle any situation, but the order to build depends on what you fight. Early you're focusing on using your E but mid and late game you gotta play like a true hybrid and use every ability for your DPS, when to use your Physical spell, your AP spell, your Auto, and your op dank ult.

For the two AP items, Rylai's and Liandry's torment, they're a serious power couple. The slow on Rylai's ensures that enemies are trapped for longer within her E and Ult, so they take more damage, and Liandry's burn scales throughout the entire game, so even with low AP all her abilities deal excellent damage, not to mention the burn is doubled from 6% current health to 12% current health on proc from a movement impedment like Rylai's. Also Rylai's makes the E an incredibly effective peel.

For the two AD items, Black cleaver and Mortal reminder, you get so much armor penetration that your Q, ult, and Autos can hurt tanks just as much as they hurt an ADC. That's 45% plus 30% (However I'm not sure if the 30% reduction from Cleaver is additive with Mortal reminder or is it's calculated after Mortal reminder's damage step. Either way it's a LOT of ****ing armor pen). Also, I choose Mortal reminder and not Lord Dominic's because stopping ANY healing, including Life steal on ADC's (Which many people forget about) is way better than a petty 10% Physical damage on tanks. If you built full AD that 10% is a lot but you're not,so it's not worth as much as Grievous wounds. With all your penetration, kiting, and mixed damage, MF can deal with tanks crazy fine. You want to make sure you can kill the squishy's faster than they can kill you. Also by reducing their healing, you significantly increase the chance of killing someone with the Deathfire and Liandry's burn if they walk away with a tiny amount of health after you fight them and they flash or something. Sometimes you can survive burns at low health by unloading all your potions, so grievous wounds makes them waste those pots too :D

Easy really. Ghost for dank kites, and cleanse if they have a lot of CC. Just gotta make sure you use your W to your advantage. Either capitalize on speed with Ghost+W active, or get cleanse and use W tactically.
You MAY opt for Exhaust, as Support MF that's the best option, but as mid you generally want to be Mobile for sick Ult ganks and ensure you can position correctly in team fights and stay away from Line breakers like Olaf and Kennen.

PROS:

Well Rounded:

With at least two items under her belt, Hybrid MF is capable of Dueling very well as long as you built the cores in an order that suits your Match. Perhaps Rylai's to kite them with W, or Liandry's to harass extremely well before an all in, Cleaver to help your ADC or Bruisers deal more damage, or Mortal reminder to stem the sustain on healers or tanks and increase your personal Physical damage. Also if you're carrying, enemy tanks find it harder to counterbuild you, as you have plenty of option to deal with almost any situation and deal both forms of damage.

One of the better Backlines:

Her W passive and active are wonderful for helping MF compensate for lag in your decisions a bit more and respond to teammate's initiations faster, as well as run away from backline divers like Olaf with your ghost because you'll always be faster when you both Ghost. Also allows her to move from position to position better.

Excellent wave clear:

Her E is an AP ability but it still hits minions and can hit an unlimited amount of targets so long as they are in range of the circle, so it's harass and farm. Incredibly efficient in lane as well against assassins with a melee auto, like that pesky little Zed. Also her ult is incredibly short on CD, so late game it's a great wave clear against Super minions. Can't even begin to count how often I clutch saved towers with an ult.

CONS:

Bad Early/Item Dependent:

You might be prone to losing lane if you're put against a champ you can't bully. You might have harass but you don't have CC and you follow ups for your jg ganks are pretty bad without an ult, which the enemy may just flash and make you look dumb. Just like as ADC, she's still item dependent as Hybrid Mid.

Depends on Team comp often:

You might wanna have someone else on your team with AP, and ideally two tanks. MF as a champ thrives off of a team with tons of frontline and support, and is crippled in use without a wall between her and the enemies when in huge team fights. A team with a strong MF, a support, and 3 tanks usually looks like an MF with 30+ kills since she can easily pick enemies off if she gets peel and enemies are locked down. However since she has absolutely no CC of her own without Rylai's (A bad first item often) she struggles without allies who can provide ample amounts for her AoE's to work and log enough DPS to carry.

Early in lane, it helps to aim your E in a way that hit both backline minions and the enemy champ to shove their lane easier. Don't use your q to poke or farm, only use it to last hit the Cannons or when battling. Try to hover your mana around 2/3rds at all times in case you get ganked or are forced to engage. Your mana runs out fast early on. Since she has high AD base stats you should have really good farm compared to your enemy laner even without AS runes or stats.

When team fighting try to stay near your tank as much as possible. Warn your Jungler that you will have bad follow ups, and try not to request early ganks (With he goal of a kill), simply employ their help to shove a lane or protect your tower while you back. MF doesn't need to win the early, and doesn't benefit a whole lot from it. You need your scaling, and efficient farm gets you that faster than betting everything on improbable early kills. NEVER FORGET TO FARM. Kills are worth about as much as making sure you get the entire wave consistently.

I mean I haven't even done this, I Main support, but if the COMP IS IDEAL (See above) and you REALLY like and do well with this, then go ahead and play this build in ranked. In ranked, teams don't surrender much so you're more likely to get your scaling in.