Ok, Im going to switch over to advice for playing against the AI as this seems to be what you are doing.
Tower eating: 1 point in the skill allos you to skip goingo back to the crystal untill you need to buy items. You dont need health potions, you dont need health regen. All you need is the one skill. Once you have it at level 2, you can easilly walk into enemy tower range, smack it a few times, eat it for health, smack it some more and watch it crumble. On a map like prison where you can take down one side of towers and be able to make it to one of the enemies portal flags, it can be DEADLY. The main point of the ability though is healing. If you cant see the benefit of having a native skill to heal yourself, I dont know what I can do for you.
The favor item you mentioned is one of the reasons I believe your playing against AI. Online for some reason, Favor is whacked. I didnt have any trouble with it for days and all of a sudden, poof, ive got no favor and no items. In any case, yes, the amulet of teleportation is incredible for Rook. It allows you to play his tower spam build (which is probably his most powerful) without wasting any money on speed items. VERY good item for Rook.
As to the Heart of Life, yes, it is amazing. On any character. at any point of the game. It is BY FAR the most overpowered item in the game as it is bugged and regardless of max hp and mana, will heal you to full so long as you dont take damage. Even if it didnt, it is still incredibly powerful and should be on every players list of items to get, regardless of demigod. IMHO it should be an 8k artifact. Not a 4k trinket.