Bear with me, I just can't help quoting E.B. White...
"Analyzing humour is like dissecting a frog. Few people are interested and the frog dies of it." 
But in truth, I'm a bit of a comedy student myself, and while I mostly prefer to just enjoy the frog jumping and croaking happily alive, I can well understand the curiosity of looking into the mechanism that produces all that funny business

I must admit not knowing Armstrong & Miller very well, I'm afraid I don't find them terribly funny, but I'll try to answer your questions, perhaps you'll be interested in a foreign perspective, although limited.
- Does the humour remind you of or seem particularly different to other comedy sketches?
- Does the language used remind you of or seem particularly different to other comedy sketches?
- Do you think Armstrong and Miller are trying to imitate any particular groups of people?
Same answer here, the feeling I have with those RAF sketches is to have seen billions of them, just about every British comedian (and some of their dogs) seem to have tackled the matter at least once, but I cannot identify any specific connection there.
I guess it's all down to Biggles, comedy parodies of a serious parody, so to speak, with the adventure part omitted and just the banter emphasized.
- Do you think Armstrong and Miller are trying to appeal to a particular audience?
No, not really... perhaps it's got more appeal for older generations (or rather "differently younger", as the PC freaks would have it

)
- What do you think of the use of accents?
I didn't notice anything specifically to comic effect there, but perhaps that's the foreign perspective I mentioned above

- Do you enjoy use of catchphrases in sketches or is predictability boring?
I'm not much into catchphrases and shit...

No, seriously, I think it very much depends on many factors, the situation, the character...
I understand the most successful catchphrases just happened by chance, rather than being planned, and are more often developed by the actors themselves rather than the writers, judging the audience's reaction while performing.
Lovely jubbly!

P.S. 2 out of 3 of your videos are blocked for non UK viewers, no big deal, there's plenty of A&M on YouTube, but just so as you know.