Attaching luan to fiberglass

Use epoxy, the same thing they use in boat building and repair. The process is the same/

Lightly sand the old fiberglass back. Remove all dust and and just before applying the epoxy wipe down the fiberglass with acetone. Only the wood needs a first coat of unthickened epoxy. Do not let that first coat fully cure because you want it to chemically bond with the second coat.

Thickening the epoxy is a good idea for the final bonding, but they you might need a notched trowel to get even coat. Clamping the fiberglass to the wood substrate is important. This will be difficult on a large are unless it is laying flat and then you can just use weights.

the strongest way to join dissimilar is two coat them with expoxy. Within several hours join them with fresh epoxy. You can use micro-ballons or wood dust as a filler to thicken the epoxy first.

It depends on what exact adhesive you use. I'd follow the directions supplied with the glue, not some random directions found elsewhere that may be for an entirely different product.

Epoxy with thickener would only need to be brushed on one surface, and then the two put and held in good contact until it sets. Some sort of a contact adhesive usually gets applied to both surfaces and partly dried before they are united. Probably there are other reasonable options as well, and they would have their own procedures.

Note sure but I'd look at the tube of construction adhesive for their recommendations.
Loctite Power Grab or PL Premium have good specs. Watch for the amount of time you have to move the item around before it sets up.
The demo videos indicate to put the glue on one side.