@@Sweenorbuilders Like Steve also asked below, that Luan is usually vastly inferior to the wood used in the Glulam beams (unless specifically graded and rated). Plus you have anywhere from 1/2-7/8 of the wood fibers running in the "wrong" direction compared to the commercial beams with a lot of luan underlayments having super thin outer plies and a thick garbage cross ply in the center. It may not matter in this case as the beam is relatively short, but it should be noted for the public that this is not a case of 1:1 substitution of a commercially rated Glulam beam. I would have used either 1/4" exterior plywood, 1/4" marine grade plywood, or 1/4" solid wood. The first two plywoods would have a greater percentage of the wood fibers running lengthwise, plus the guarantee of an exterior rated (and structural) adhesive between the plies. Marine plywood would generally be guaranteed to be void free. Solid sawn wood has 100% of the fibers running in the correct direction, no voids, and no mystery glue to deal with.
Depends but most of the time the engineer just says how to build it and out of what approved materials just like the rest of the house. An engineer isn't going to come inspect how you built your floor he's just gonna provide the plans, same for this. Unless the local building and planning department says otherwise.