I I basically take conqueror almost every game because you always want to stay in fight as long as you can. Phase rush is good as well but you got less healing in exchange for speed that allows you to get sticked to somebody. In overall you should just practice and check what is more confortable for yourself :3

There are 3 most common mythic items for hecarim. Most of people take chemtank into phase rush and divine/trinity into conqueror. To be honest the best choice for almost every situation is divine for my self. You got all you need from this item. The damage, healing, ability haste and ar/mr pen. Of course there some exceptions I mean when your team is too weak or just being oneshot in teamfights then you go for chemtank. I advise against playing as hecarim frontlaner because you want to be carry 1v9 machine every game. Same situation with trinity force imo that item is just too overhyped.

You always want to keep your Q stacks up. There are a lot of videos that shows you how to do this and make your clear healthier and faster. There is a link (not mine but gonna do my own too :p https://www.youtube.com/watch?v=lJ2UlfS_gqc&ab_channel=Doaenel