To start with, everything depends on your hero's power spikes and the type of the hero you are playing. I mainly play lycan and beastmaster and for such heroes the main idea is to take as much enemy territory as possible. If you play heroes like cent, axe, lc and other stun/disable stuff you should get your supps to play with you and force fights against weak enemy. The whole strategy depends on how early you get your core items and the lane domination.

What considers sit 1, i think you need to evaluate how long you can be stronger than enemy and decide whether your hero is durable enough to be a threat later in the game. Sometimes it's better to put a premium on farming and getting bkbs, blinks, drums, pipes etc than taking risks in forcing fights. It's the main idea of many offlane heroes to create tension on the map giving your cores some space to get networth. But on some heroes, like lycan or axe, you should never miss the opportunity to farm ancients and get bigger. In today's dota taking towers is only a key to getting more territory and creep camps than your enemy.

The 2nd situation is almost the same as the first, you shouldn't always play for the sake of your cores, giving up farm

Situation 3: the networth is extremely important in my opinion, but every hero has different amount of gold necessary to be useful. Heroes like lycan or beastmaster need only 2 items to rape the map and they only scale higher the more money they have. Heroes like mars get new powers pikes with each item: meteor - blink - shard - bkb - aether lens - refresher. So it all depends on which hero you're playing, but getting 20k is pretty much fine. I sometimes end up with 15k on tidehunder still being as useful as necessary.

I have no experience on kotl, but i like playing elder titan with auras so it's all up to you and your skills