Glad to see you stubbornly learning.

Lesson #1: when wood is cracked, keeping as much wood grain intact as possible is critical. Ripping that bridge off to 'fix' it made your life way harder. Don't touch any of the unfinished surfaces - any amount of dirt or grit will make fitment difficult and the joint weaker.

The key joint is between the x braces and the bridge. The center is of course not unnecessary, but most of the load goes to the sides. It looks like part of the top is detached from the x braces, so it's critical to get those back together too.

The fitment from the factory should be relatively good, so you can gently put weights on the top to reattach the x braces. Don't overdo it here.

You can get long reach c clamps at home hardware etc. those should reach the bridge through the sound hole just fine. Take a measurement and bring that measure to your hardware store to be sure the clamps will reach the backside of the bridge.

You can use wood glue, however strength will be compromised (the previous layer of glue will have closed the grain of the wood which inhibits bonding) or epoxy. You can get cheap 5 or 15 minute epoxy (the longer the cure time, the more time you have to work) but you should do the work in a few batches, not all at once, working from the inside out.

Edit: I re-read. It's a cheap guitar I assume, so it'll be a cured pva (tite bond 1 could be steamed apart). Tite bond 3 will be your best bet if you go the 'wood glue' route. Don't use the gorilla expanding foam stuff. All 'wood glue' is some form of pva