The third gear issue is most likely worn out synchronizer for that gear. Which means the others wont be far behind. I have about the same mileage and all my synchros are gone. As in when I changed the oil in the transmission a whole bunch of brass flakes drained out in the old oil. (Synchros are brass rings).
The good news is with a little practice you can pretty much shift to any gear without synchros and without grinding. I grew up when lots of vehicles still didn't have synchronized transmissions and you learned to work them. For my YJ which has the same AX-15 transmission, I shift to 2nd at fairly low road speed but a quick flick of the shifter. Then shift to 3rd requires kind of a pause going through the neutral gate. If I rush it, it grinds. That sounds like where you are at wear-wise. Shift to 4th is gentle, not hurried, not paused. I rarely get into 5th since the vacuum gauge I mounted tells me that up to almost 70mph I'm actually making more efficient power with less throttle staying in 4th.
Shifting back down depends. If coming to a red light or stop in any gear I shift to neutral and let the clutch out while braking to a stop. If slowing for a corner or vehicle in front of me I usually get the smoothest downshift by going to neutral, letting out clutch, then after slowing the Jeep judging which lower gear I need and then clutching and gently into it. The purpose of all this is to try and match the relative speeds of the different gear shafts involved when shifting. Which is what the synchros do by friction until they wear out.
Go ahead and change the oils in your transmission and transfer case for peace of mind and to see what comes out (especially since the front driveshaft may have been disconnected for a reason). Note that the spec for transmission changed way back from heavy gear lube to 10W-30 motor oil. Check the FAQ thread to find write ups with good tips on changing the fluids (and the discussion of the gear oil spec changing to motor oil).
Good luck and have fun with it. This forum has a wealth of knowledge already written up and stickied which saves having to post a lot of questions. But when you do have to ask, there's lots of help.
Edit: I forgot double-clutching. I don't have to do it much. But if I get stuck in neutral after coasting/slowing or pausing too long in a slow shift, a quick in-out-in with the clutch helps spin up the gear shafts so it will go into gear.