You do not need to clean the brass after trimming. You do need to chamfer and debur.
I will let others chime in on questions 2 and 3 as I do not reload with a progressive (though if I could get a nice Dillon for half price, I am sure that I would put up with my wife's unhappiness for a bit). But for me, single stage loading, I do it in these steps for my rifle brass and skip the lubing for 45 ACP (my only pistol reloading at this time):
1 inspect cases for damage and wear
2 decap fired brass with universal decapper
3 clean fired brass in stainless wet tumbler (I do this after decapping because the stainless does a great job of cleaning the primer pockets for me)
4 dry cases
6 lube outside of case and resize
7 wipe lube
8 measure brass and inspect
9 trim if needed (when I trim, I do the whole batch at one time and bring them all back to minimum spec even if just one is over maximum spec)
10 chamfer and debur if trimmed
11 mica lube necks and flare case mouths
12 wipe off the mica if I have made a mess - leave it if I have managed to stay conservative with it (dry lube like mica or graphite will not harm the powder or primers)
13 prime cases
14 charge cases
15 seat bullets
16 crimp (I have the same RCBS die set that you have but I seat and crimp in separate operations as I am sometimes switching back and forth between bullets and I am just doing small batches. If I had a progressive or was doing many more than the 50 or so that I do at a time, I would set the die to seat and crimp in the same operation.)
17 final inspect and wipe down
shoot and repeat!
You will notice that some of my steps are out of order compared to my favorite reloading book, the Lyman 49th. You will also note that the way I do things will not work in the progressive as it will disrupt the progressive operations.
Others will come along and tell you the right way to do it in a progressive, but if it were me I would only use a progressive on rounds that I did not have to deal with lubing (like the pistol cartridges). But again, I am a small batch reloader when it comes to my rifle rounds.