In general, any recoding of video will degrade the quality, but if you set the bitrate to a suitable value the difference will probably be not noticeable. If the filesize after encoding is about the same as the original, then the bitrate is OK. In Avidemux, click configure under Video Output to get to bitrate, 1 pass/2pass settings etc.
The business with I frames is worth getting the hang of, because if you cut on I frames the output is just a 1:1 copy of the remaining scenes, with no loss of quality (and is fast). The distance between I frames is different for each movie (it's set by the person who encoded it), but is usually about 1 sec or 30 frames approx. Obviously the cut points for your edit will probably not fall conveniently on I frames, but if you can live with that, it's the best method for editing.
My approach - say you wanted to save just one scene from a movie -
load the movie in Avidemux
press up and down arrow keys to get to the scene start
click B, then del to remove highlighted 1st part
press up and down arrow keys to get to the scene end
click A, then del to remove unwanted highlighted last part
if you only moved the position using up/down arrow keys, the cuts will be on I frames and the settings can be left on copy (it shows I, P or B frame at the bottom of the interface). Click to save, and it takes about 3 secs.
If cutting on I frames is not accurate enough, use L-R arrows for 1 frame at a time and encode the result (longer).
I often use a mixture of copy + encode eg if a movie has low audio volume, I leave the video on copy, click audio Filters and set the gain to (say) manual +12 dB. When I save, the audio is boosted (recoded) and the video isn't touched so is identical quality. You can even shift the audio in millisecs to fix out of sync movies.
Sorry for long reply.