Should we have stayed grouped because we had no split pusher?
I've actually won a lot of games from behind. Skype buddies always trying to pull cool stunts early, me derping out and giving FB by trying to pull cool stunts early.
Solid communication for one is going to make a massive difference. It will let you plan out appropriate strategies and execute them.
Vision makes a massive impact as well - supports can only plop down 3 wards now, so if you're covering a lot of ground as a jungler it's extremely helpful to expand vision. A lot of assassins operate like Kha'Zix where they're really good against isolated targets but ~meh in team-fights. If you have solid vision control, then your team-mates know when someone is truly isolated and can capitalize on it, and they can also see enemies moving around and (hopefully) won't get caught out.
Pro pick strats and anti hostile pick strats in one.
As for team fighting - if you have champions with amazing utility and area-effect damage, you can often win team-fights when behind. A lot of champions known to pub-stomp, (most assassins or anything with an assassin secondary) are pretty solid at the 1v1 thing but not well suited to large 5v5 engagements. Most mages, marksman, supports, and tanks are more well-suited to grouping up then fighters and assassins.
This is my general default strat because I'm a support main and often face teams where everyone's trying to carry and has ~eh supportive qualities, but if you're running no utility/high damage champions like Kha:
Stall tactics are what you default on. Split pushing is more something you do when you're even or ahead, as when you're behind the enemy team can often shut it down with very little effort.
Also - split pushing tends to rely on a fair deal of communication to execute well on. The ultimate goal is to force enemies to constantly choose between loosing a tower or dragon, top tower or bottom tower, something like that. If they can crush the split-pusher and crush a 4v4 you're not making them choose anything.
With Kha'Zix stall tactics - I'd assume you'd mostly want to concentrate on safe wave clear with void spikes. Without team-fight superiority, you're goal is to turtle the game until the gold/experience difference is to small to make much of a difference and then try to make a play.
If you can clear minion cover away from turrets and stick together as a 5 man team, it's generally going to be quite difficult for the enemy team to make much ground. They can dive your team under a tower without minion cover, fighting with a clear disadvantage, or try to pick away at a tower from relative safety.
If you stall long enough - you can get all the items you (and your team) needs to make the plays.
For Kha'Zix's perspective, those plays are going to be reliant on ward-coverage picks.
As for who you want to target - depends on the ward coverage. You want to at least force a 5v4 so you have a 1 man advantage - so if you can take out a support, take out a support (most are pretty game-changing in team fights as well).
Tanks are the most high-impact champions in a team fight, but you'll often just give a free initiation to the enemy team and goad your allies into focusing the tank if you try to catch them out. You need all 5 members late-game for that to work.
Mages second - poke means amazing pre-fight power and turtling after a lost fight, AoE means team-wide pain, and many come with AoE CC for painful team-lockdowns. The reason marksman are focused instead is because killing a mage in 2 seconds still allows a QWER combo, in 10 seconds it's like QWERQ. Killing a marksman in 2 seconds means 2 seconds of AA, in 10 it's 10 seconds of AA.
Supports amplify everyone else's power, and often bring a ton of power to a fight.
Marksman should be prioritized outside if they have to much protection in a team-fight to take out in a team-fight.
And fighters are lowest priority.
If you can make a 5v4 happen, make it happen though.
