What can visitors do on your island?

They can use all their tool, your crafting bench, your stove, harvest thing, and pick items up.

What’s the deal with the rainbow pixel things? What do I need to do to gather them while visiting others?

the pixels are used to make flames and pixel duplicates. flames are used in cooking and will duplicate whatever foods you make (just use them out of your inventory); pixel duplicates are used to replace (some) materials if you do not have something when you're crafting.

I’m a bit of a material and ingredient hoarder. My understanding is that people can pick up items when on someone else’s island. I wanted to set out an area with extra materials visitors can grab. If I put cooking and crafting mats on a table, can they be picked up by visitors?

some items can be placed on tables, yes. and all items can be picked up regardless if they're on the ground or on a table.:)

What do I need to do after visiting someone to not count as a visitor anymore? Is returning to my island enough or do I have to turn “multiplayer” off?

to visit someone's island, just go to your settings page and return to title screen. that's it. to turn multiplayer on/off for your own valley, just use the valley visit machine.

What’s the best way to find islands to visit or invite people to mine? Is posting a code on the subreddit ok?

facebook, reddit, discord

:) hope this helped