Fishes and bugs can be sold to CJ and Flick for 1.5 times the normal price that you get from Nook's Cranny. Since the two vendors visit on random days, can I invite friends over to sell their fishes and bugs for extra profit? And if they can, do they each need to complete CJ's challenge, or do only the host need to?
Apparently no. CJ never gives the option to sell fish or purchase collectibles to visitors. He just remarks about how you're visiting from off-island, should ask a local for good fishing spots, and that he'll be doing his show here for a bit and will catch back up with you when he returns to your island.
Unfortunately the visitors cannot sell to your CJ and Flick, even if they have met them before on their own island.
My wife found this out the hard way, she had 40+ tarantulas to sell, and got excited when our friend who plays mentioned he had Flick on his island today, only to be disappointed when she brought them over and couldn't sell.
Another note, insects and fish are different to furniture, in that they cannot be dropped (link goes to screenshot).
If an item is Dropped, it can be picked up by anyone.
If an item is Placed, it can only be picked up by whoever placed it.
If you try and place an insect or fish on another island, there is only the "Show Off" or "Release" options, which either gone to the void never to be seen again. (This also occurs if someone else is currently visiting your island)
For comparison, here is a screenshot of the options a furniture item provides.