I haven't played khazix in a long while but I used to be a khazix main so here's some (probably not as good) advices:
You can flank and take down the carry in the back line, even if they're not fed but you should always prioritize a fed enemy if they're not a tank (use ult -> E + combo)
As an assassin, don't expect to start the fight; you clean up instead. either wait for that 1 v 5 penta kill clean up (not recommended) or
Wait for the perfect time to start your "snowball" aka E resets: it opens so many possibilities for you
BEFORE GOING INTO A FIGHT, PLEASE PLEASE CHECK THE ITEMIZATION OF THE ENEMIES TO FURTHER CONFIRM YOUR TARGET PRIORITIZATION
To recap, the only reasons to go into a fight:
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Flanking a carry (but you must let your team start the team fight UNLESS scenario [3] pops up, which then you can sacrifice yourself to kill the carry if they're that big of a threat--but you won't die if you can E out) make sure to flank from a wall so you can leap/escape over that wall to lower the chances of dying.
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Securing a kill (i.e. joining in on the fun after it has been communicated in your team that the thank engager will attack the enemy carry or something)/securing your snowball (e resets)
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Assassinating an isolated target
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Cleaning up
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Wait for CCs to be used on your tanks
Other than that, stay back line and wait.