Should I give up on this TJ?

This would be my approach. First, understand what your two main issues are - frame rust and torque box rust. They can both be dealt with in several approaches, depending on what you want to invest in time and money. Apologies in advance but I am making the assumption you are new to Jeeps like I was before I started restoring mine, so I will explain like you have no knowledge or experience with Jeeps.

Frame - doesn't look that bad, need to remove skid pan to really know extent of rust. You will probably lose a nutsert or two in the process (threaded inserts in the frame that the bolts go into). I bought mine from Black Magic Brakes - fast, affordable, great to deal with. Make sure you support the drivetrain safely so you can get under there and get a good look. Most frames rot on the in-board side of the frame and between the frame and the skid because it is hard to wash out the trapped salt from those areas. Wire-wheel it down to bare steel and look for cracking particularly around the holes in the frame. Also check the rear frame section where it arches up over the axle. Notorious area for rust and cracking. If there are rust holes or cracking, look up Safe-T-Caps as the cheaper alternative if you have access to or skills as a welder. Seriously consider how hard you plan on wheeling your Jeep. IMO these are fine for a daily driver/mild off road, but I am not sure I would trust this exclusively after seeing some of the crazy stuff folks on this forum run their Jeeps over! If MOAB is in your plans, jump right to a new frame.

Torque box - the floors of the Jeep are spot welded to long channels called torque boxes that are then bolted to the frame. This seems to be where yours looks the worse. There are 11 bolts holding it all together. The main bode of the tub has 3 on each side and generally the issue is with the last two on each side. Like the frame, you have two options, cheapest first. There are sections available called Rust Repair Patches that you can buy to go over the rusted bolt area. These require you to jack up the body, cut out the rusty section and weld these in place. On mine, there was not enough left so this wasn't an option so I fabbed a new, much stronger torque box section out of 16ga sheet metal which is thicker than the factory. Instead of simply spot welding it in place, mine is plug welded and perimeter welded in place. I also made it wide enough to allow the roll bar bolts to secure it to the floor, adding additional strength. It is not coming out but certainly doesn't look "factory". The other option is to replace the torque boxes completely. There are about 4 bazillion spot welds holding it on, time consuming, but not "hard". It will cost more obviously, because the boxes are a couple of hundred each. It will then be factory in appearance.

It looks like you have a nice garage and if you can find some friends willing to help out, if is completely doable. Yours is much better than mine was!! Feel free to ask me anything along the way, I am just wrapping up the same type of repairs.
 
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manatsu- welcome to the family. Your rust is not bad, I can tell you that i have used a coarse wheel in a drill and hit the frame. it sucked, but once i got the thing all cleaned up, i hit with some protectant and i also used a spray wand and treated the inside of the frame. Lastly i drilled a drain hole in the frame of my AMMO can TJ and it has helped. My DD sahara is not so lucky. I will say that ohio is bad with salt and rust.