Mess with the brakes, they are not complicated and you will learn a lot more about your Jeep from working on it. A 1970s CJ has a very ordinary Girling type hydraulic system with or without booster and the only fiddly part is bleeding the master cylinder.
The plate can be knocked out sideways if it does not come loose. A screwdriver and hammer will do it but choose a cheap screwdriver as it is not the best use for a screwdriver.
The whole caliper is supposed to be able to slide from side to side so the plate only stops it from coming up. If you are not removing the hose (which you would not do for a brake pad change) you can suspend it on a piece of string from the suspension, just do not stress the brake hose. If you see any signs of cracks in the hose, particularly where it bends, it is time to replace it anyway.
You should be using a correct brake spanner, not an ordinary C open ended spanner, on the brake pipe fittings and bleed nipples. Those suckers are soft and easily rounded if they do not want to give. a brake spanner is almost a circle with a small gap to get it round the brake pipe, you can pick them up at any good auto spares outlet for a few bucks.
If you want to rebuild the caliper or check the inside for corrosion you can take the pistons out of the caliper by applying brake pedal pressure. Once out you can examine the bore for pitting and put new seals on the piston or if pitted you can replace the caliper. Just remember to lube the seals with the correct brake seal grease before putting it back, do not use ordinary grease and make sure NO DIRT gets in there before you fit the dust covers. You will have to do both sides to get even braking but beware, there is a left and a right so do not get them mixed up and do not kink the brake hose.
Brake pads are easily inserted but if you are just changing pads and not seals you will need to lever those pistons back to get the clearance once you have the caliper off the disc. I open up the bleed nipple and drain some fluid from the caliper as it stops the reservoir at the master cylinder from overflowing and the fluid at the caliper is always the oldest in the system.
Once it is all back together you can think about bleeding the system through with fresh fluid, a few bucks but it will replace the moisture absorbent gunk in there. You need to read the manual on the correct procedure (including the Combination Valve being held open) as they are bled at the four corners in a sequence. furthest away first.
It is preferable to have an assistant for the bleeding, my wife hops in and then gets confused over UP v DOWN on the brake pedal but it is always fun. In fact it is always fun to have company when working on the Jeep but my boy is only 2 years old and gets the 1/2" spanner mixed up with the 11mm so the wife it has to be.
If you finish it and have a hard pedal and it does not pull side to side on braking it is good to go.
The rear drums hide the brake wheel cylinders. They can leak, burst and generally mess up but are only a few bucks so if I take the brakes apart I have new ones to hand. The self adjusting mechanism is also known to give up but if you can get the rear drums off (and they can be truly stuck, slacken the brake adjusters and hit them with a hammer round the edges) it is fairly easy to replace the parts or if they are in good condition to work the screw back and forth. The springs can flummox most people so get a diagram of where they go and do not lose the little screws on the drum face that locate the drums, they often are lost and it is a PITA as the drums can start rubbing and squealing.
And the very very last thing, when you work under a Jeep ALWAYS have it supported on a proper axle stand on a level floor with the wheels chocked and preferbly have the spare tyre under the frame as well. They will slip off a jack and many a home mechanic has been lost in that way. If I work on mine by the side of the road teh spare always goes under he frame and it is lowered down on to it (PS I see skizriz has reproduced one of your pics below which IMHO shows how not to do it, a jack by itself should be avoided and you are risking losing a foot or worse if that is all that is holding up the corner of your Jeep).
Good luck with the brakes, you feel them every time you touch the pedal and are very satisfying to get right.
BagusJeep lives in Bali.
1981 CJ7 258ci - Bagusjeep
1984 CJ7 258ci - Puthijeep
1981 J20 258ci - Gladys
1951 Willys CJ3A/MB/M38 - Little Willy
1995 Cherokee 4.0 - CHEROKEE