Can you add a spell to a magic item or feat without it having charges or at will? I can't seem to figure out how. I want to add a spell to a homebrew item or feat, so the player has it to cast as normal (using a spell slot, no limit per day etc.)

Nope. You can only add spells that can be cast normally with slots via subclasses & races, not with feats or magic items.

 are you worried the player having an extra slot or just wanting them to be able to use it more than once a day?

If it's the second thing, just let them use their slots to be able to cast the spell too, that's how the fey touched feat works.