Are all the games important for the main story. The only one I've played before is Chains of Memories on the GBA.
Don't worry about it too much, chances are you won't understand what's going on even if you do play the side games lol.
Yes they are. Even the mobile game adds to the lore. And the storyline is huuuuuuge.
If you want to understand the story properly you'll want to play all games in the series for sure. The "convoluted story" meme probably came from the fact that there were like 11 games that had major plot threads in the full story but most of them weren't being played - likely because people were treating them as filler spin-offs, or were locked out of playing them due to the fact the series games branched to four separate portable consoles.