>> 1.Liquid nails to attach the track,fiberglass,and vinyl...is it safe?!
Dunno. What does the Materials Safety Data Sheet for it say? I suspect that once it's cured it will be fine.
One question: what type of track are you using? Are you sure Liquid Nails will bond it? I found that the plastic tracking I used was pretty glue resistant...
>> 2.Should the glass track be attached on top of the litter dam and the inside top of the cage,or is there a better way?
What other way is there? I ran rails across the bottom and top of the front opening, then attached the tracks to both. Bottom one keeps the litter inside, top one hides (at bit) the lighting and heating fixtures.
>> 3.What's the best/safest glass to use,and how to calculate glass size?
Do you want the absolute best, no matter the cost? Or do you want to know what most people use?
Again, it probably depends on your tracks, to some degree. The track I bought gave a formula for calculating the size of the glass. It was designed for 1/4" thick glass. I just bought normal plate glass. You could also consider some sort of acrylic (which may scratch easily or discolor over time) or safety glass (=$$$).
>> 4.I was thinking of using Kane mats for heat,can several of these be run on 1 thermostat?We I be better off using 11" heat tape? Thanks for any and all help!
Which thermostat? Add up the wattage of all the heat mats, then compare that to the maximum wattage the thermostat can handle.
I'm not a big fan of under-cage heat for wooden cages. The glues in plywood probably aren't as bad as MDF or melamine, but I wouldn't be encouraging them to heat up, break down, and offgas. That means putting the heat source inside the cage. I probably wouldn't do that with heat tape; just too many opportunities for something to go wrong.
Have you thought about using radiant heat panels? They'd be my preferred heat source...