How long can I keep sauteed onions in the fridge

You can also preserve herbs by wrapping them in damp paper towels (either completely or just around the stems) and then placing the bundle in an open plastic bag (or one with holes poked in) Replace or re-wet the towels when they get dry. It's the equivalent of a vase without the worry about it spilling.

I use "one step" to sanitize bottles and caps, like you would do for beer, and bottle my infusions in that, and they've lasted >3 years. I've done raspberry and cherry vodka. If the alcohol percentage is high enough, it will kill bacteria or mold, so it's pretty safe for long term storage. Probably depends on the final alcohol percentage though, like if you add enough juice that the percentage goes less than 10 or so percent, you have to have more precautions in sanitizing everything. I usually sanitize anyway because it can't hurt, and I already have the equipment to do so from homebrewing.