A lot of what you can have them do depends on the tone of your game though... What are you going for?
Short answer: Megaman X + Zelda series + Monster Hunter Lite.
Long answer: Sort of action adventure game where traveling and exploring the overworld means fighting enemies and finding secrets while getting to the dungeons. The player can loot the enemies for items that can be traded for secret skills for the player or the sidekick. The dungeons serve as puzzle + exploration areas and the enemies are rare. Some dungeons might've end boss. Not really Metroidvania as returning to older areas is to get optional secrets.
I originally made the sidekick just to carry a lantern in dark caves, because I was too lazy to make a separate animation for the player. Later it evolved to bird that can use some items the player can, and then items only the bird can use (like the lantern).
After making this topic, I decided that the bird should learn skills too, like attacking and carrying the monster loot to finding treasures.
Some of these skills are passive, like the attacking and treasure finding, and as the bird doesn't collide with the player or take damage, there's no harm to allow it to attack. Other skills are active and selected quickly by the player in Monster Hunteris "item" selector (hold button down, scroll the items, release button to choose it) or context sensitive by using sort of Zeldaish action button. I believe this is the best way to keep it simple and quick, in order to keep the momentum of the overworld parts and to not annoy the player in the dungeon parts. So essentially, the sidekick is controlled with two buttons, the item usage button and the context sensitive button. If some off the actions need item usage, I'll just make it auto-choose the item for the player.
Phew...
Also the RE5 thing is probably in reference to how useless and counter-intuitive Sheva was. She almost never got helpful shots in, got in the way of bad guys spectacularly (if she died it was game over) and having to manage the nonsensical two person inventory system through a little orchestra of dropping, swapping, using, equipping, etc, was more frustrating than it needed to be.
Ah, so basiclly, every "helpfull" sidekick ever?
The item systems sounds awfull too.