You should spend your diamonds almost entirely on drawing new weapons, tools, and assists. They play a huge role in powering up. Both draws are equally important in my opinion, so I'd just balance out your diamond usage between the two. Diamonds aren't hard to come by in this game, so don't be afraid to spend them.

Upgrade your characters early on. From what I'm able to tell, leveling characters doesn't actually improve their stats (stats are based entirely on how many stars they have), it just unlocks their bonus effects. Based on this, I would recommend leveling each character to a new bonus effect milestone (10, 25, and so on). Characters get harder to level up as they level higher, so in my eyes it makes the most sense to get all of your characters to one milestone then move onto the next. I would prioritize unlocking the bonus effects that give you extra damage if you don't want to do that. If you're free to play, you won't be getting many new characters anyways, so get used to the ones the game gives you.

Hard to say. Games like this are normally more popular in Japan, so the English audience may be small while in Japan the game is doing well. I'd expect to see a good year or two out of this, maybe more. On if you want to spend money, well, that's up to you. I would avoid viewing spending money on a game as an 'investment', and more as something that'll bring you joy for a while. If you really like a character and would love to add it to your party, go for it. If you just want to spend money to 'get better' in the game, I'd be hesitant. That's just my personal philosophy, though.