I am going to install 1/2" engineered floor, I am laying down another 3/8" plywood on top of existing 5/8 subfloor to build up height to be even with tile in other rooms. Does it matter if I use Fir or spruce plywood for the extra subfloor?

If you could tell the difference you might have a PhD in wood engineering. Fir is stronger than spruce but they are often mixed. I might be able to find the technical pdf on that, it may take me a few days to look through my files.

No it does not matter.

It really doesn't matter. Go with CDX grade, ( least expensive, and does the job). I would MC the ply before installation,( it's not always as dry as perceived to be).

I was just running around the other day at box stores checking on plywood for a job. Seems CDX is getting hard to find. I found Lowes has RTD and ULX only, the store guy says it is all exterior glue in it. I have a file some where on the different names of ply. But he could not answer which was better. Now I gotta go find that file.