I added a ball valve for the skimmer outlet. Everything is fitted together.
Do I have to glue it all together or can I leave it as?
How long does the glue have to cure before its safe to use in the tank?
Yes you have to glue it, and depending on the product, it will take several hours to cure. I would wait 24 hours before running any tank water through it. You don't want any toxins getting into your system.
I usually wait about 30 minutes after gluing PVC together before using it. It won't hurt to wait 24 hours, but not necessary IMO. Do whatever you are comfortable with.
Like Heath said, Teflon tape all threaded connections, and use hose clamps on all tubing to barbed connections. I noticed you had a nylon barb in the setup.