AVCHD-Format

Yes.

Yes it will work, as long as you shoot 30P or 30i (also known as 60i).

60P will not work unless you use a third party program to process it before importing to iMovie.

If you are in a PAL country, 25P and 25i (50i) will work, but 50P will not.

I'm using a Sony RX100 and usually capture video at it's best quality setting of 1080 50p.

Aperture can't see the related "MTS" files. Howcome?

Importing the "MTS" files is a seamless process with Adobe's Lightroom.