His own agenda is tied to Blackbeard, it's the entire point of joining that crew. He will fight for Blackbeard and fall with him, being the arc's Linlin to Blackbeard's Kaido.
1) Because they both benefit from it, but while Kuzan's intentions are noble, Blackbeard's are the complete opposite. Unlike Kaido and BM, who both just had selfish interests
We have no real way of knowing his exact strength, but Koby was able to one tap a mountain sized fist. That strength came out of no where and it is likely the tip of the iceberg. There's no point in Oda buffing Koby up in that scene if that isn't coming back around later.
2) We do, that "one tap" took everything he had. And yes, he will get much stronger, but he is still far away from reaching the level of even someone like Zoro, if currently he only has enough strength to destroy 1 mountain sized arm.
Yes. I think he'll fight his fellow apprentice, who just defeated their master.
3) Which is a problem, but Kuzan does not represent injustice. Quite the opposite, his current character arc is that he is finally thinking of himself, doing what he believes is right instead of lazily going with the system
Because he's a Blackbeard Pirate and has staked whatever he wants to accomplish on Teach's success.
ONLY as far as it serves him, but as we do not know what his goal is (only his intentions), we cannot assume he will stick with Blackbeard until the end.
And that panel, which mirrors Akainu vs Whitebeard, clearly implies they will NOT be friends.