First of all, try using OBS or Xsplit to record - I'm pretty sure those programs can do the same thing as Bandicam.
As for audio, it's not all about frequency - for YouTube purposes it'll be fine if you use 44100 Hz at 16bit depth. Any audio editing program can convert these values, so as long as those values are the same between the audio clips, as well as the format in which the audio is recorded, the actual "quality" part i.e. the bitrate of the audio doesn't matter. As for cutting and merging audio streams in post processing, I prefer Sound Forge, but it's not free - Ocenaudio or Audacity should be just fine as long as you keep your audio uncompressed.
And here's another hint - if you already separate audio and video streams, make changes to both and compress them, then use a muxer to merge the two streams instead of compressing them further.
I know this sounds a bit confusing, so let me make it simpler:
1) Always record both audio and video uncompressed (high bitrate MP4 for video saves you additional rendering and compressing if you want HD on your channel - WAV is a great format for audio) with Xsplit or OBS
2) Edit your video the way you always do, save it without the audio stream in MP4 (I assume you use the H264 codec)
3) Edit your audio and save it as MP4 (alternatively, as either AAC or M4A; for YouTube 192kbps is fine)
4) Use a muxer (I recommend MKVToolnix, works with MP4s the same as MKVs) to "mux" (merge) streams together and you're done