Here are my questions:
Do you think I'll be able to iron this fabric onto interfacing, just as I would for a regular t-shirt?
I think you could iron it fine but I'd use a lower setting than you would for cotton so there is no chance it will melt.
Anything I should be fore-warned about, when working with this fabric?
You might find that it frays when it's cut so be careful in how much you handle before you get the interfacing ironed on.
Sometimes the fabric is... meshy. Do you think I should layer a solid backing sheet (between the shirt and the interfacing?)
I think the interfacing should give it enough stability to use it alone.
Do you think it would 'look' ok (and does it truly matter?) if I mix hockey shirts with t-shirts on the same quilt?
I don't think it matters - if that's what they want (a mixture) then that's what you should do.
Good Luck and be sure to show us the results!