You need to replace the wheel hub cover, looks like it's messed up
True but will not affect his current MOT issue.
Re the Torx or what ever retaining screws I have often had found them to be damaged and in general a good centre punch at the edge of the screw can be used to tap the screw around to undo it if the correct tool doesn't work.
Re the self adjusters I suggest you have a good look at them so you fullly understand how they actuate before attempting to manually adjust them.
As has been mentioned handbrake cables, a good idea to replace. Once you have them fitted, but slack I suggest you manually if possible adjust the brake shoes and clean off any dust etc. so that the drum will just slide over them, then give drum a light tap to square it up , the drum should still spin easily, press the brake pedal several times to square up everything and if shoes have correctly been adjusted brake pedal should be firm but drums still able to spin when foot off pedal.
Caution do not over adjust them and bang the drums back on or it will be seized and very hard to remove the brake drums!
After all that only then adjust the handbrake cable, I try to aim it to lock the back wheels enough to tighten the wheel nuts/bolts without the wheel turning on about three clicks, but it must be totally free when handbrake off, also the braking effort must come on equally on either rear wheel as you raise the handbrake lever one, two or three clicks indicating the shoes are correctly self adjusted in the brake drum. If entirely happy only then road test using foot and hand brake and on return check no wheels are unduly hot indicating a brake binding and ideally jack up and recheck by spinning the wheels as before on handbrake application. You may be able to adjust a fraction more then, but don't get too keen.

Re the grease caps they are usually available at motor factors or online, also unlike the old days with adjustable hub bearings and lots of grease they are sealed so unlikely to be contaminated by a damaged grease cap, although good practice to replace if damaged.
