The Hungarian sentence here feels a little off - "Ez egy nagy szálloda" would be a more correct way to say "This is a big hotel".
"Ez a szálloda nagy" would sound nicer as well, but that literally means "This hotel is big".
Either way, "Ez nagy szálloda" doesn't really sound natural in most cases.
it's actually neither - it's called a palatal stop (or affricate depending on the linguist you're talking to). it's closer to a "d" sound than "j" or "g" but still not quite a "d." Anyway you asked this a month ago so i'm guessing if you've stuck with it you'll have found out by now. As for the "y" being silent, it's because it's actually a digraph, so "gy" is treated as one letter, much like how in English "ch" signifies just one sound, not two.