You can change the tray behaviour in the “Advanced Rainbow Tool Settings”, but shouldn’t have any impact on performance, it checks for an update every 10 mins, that’s all it does in the background. Main reason for the tray was for the game launch options from the tray icon.
If you’re coming from PoE/Diablo, item generation works differently here. In short, an item can have a prefix and/or suffix, all parts of the item have their own rarity and it takes on the highest rarity, so a white item could have a magic prefix and rare suffix and the item would be rare, if a rare item has a magic prefix and no suffix it is still rare. Rainbow will show you the different rarities of the parts rather than just the end result.
Skimming through it, this looks like something you would want to read: