Yes; they are. You can do the whole thing with freeware solutions.
I know Virtualdubmod will also do the resizing, but the application Moth3r mentioned sounds interesting.
As you are using Adywan's AVCHDs, the audio should already be DVD compliant. I recommend you convert from AVCHD to NTSC not PAL, as the audio will be then be done already and it will play in your player; you just have to convert the video.
As an MPEG-2 encoder, you should use HC Enc. It is great quality and free.