Bike re-assembly gear and noise issues
First thing to do is check the rear wheel bearings. Get the rear wheel out and inspect the axle. If there is any play between the axle and hub or roughness or 'notchiness' when you turn the axle, the bearings are worn out. If you have a cup-and-cone style hub the bearings can be serviced. There are several online resources that show you how to do that. I recommend Park Tool's articles and YouTube videos. Some hubs have replaceable cartridge bearings.

If the gear shifting is not working, that could be due to a number of different things, including the issues with the shifter, but most likely poor indexing adjustment. Again, there there are number of online resources that show you how to troubleshoot and adjust indexing.

I note you have an older Shimano Tourney, which is is lowest level Shimano groupset, which does not offer great shifting in the first place.