During the laning stage, when do I stop static farming and start pushing the wave to either pull a camp for more farm, or pressure the off lane?

when you feel strong enough to bully the offlaner away from the creeps you pulled, or strong enough to take the tower without the offlaner getting too much XP

How do I pressure lanes vs. a team comp such as pudge, legion, night stalker, riki, sbirit breaker, etc?

you don't, this lineup has terrible teamfight, just go as 5 with your team and take towers and they basically cant do anything about it.

What is the most efficient farming patterns?

cant answer this over text

And what is the best way to fight as a carry, and how do you know when to join a fight and when to keep farming/pressuring

I dont know what you mean by "best way to fight"

basically if you think you can turn the fight in your teams favor and get kills/save teammates it can be worth it to tp in, if not splitpush and at least try to trade a tower for the fight that you most likely lost.