The best is to use an elementary stream to import into Avidemux.
That is video and audio separate. You will import only video (mpeg2). Than you click on Video/Copy and choose DVD (lavc), than configure and choose what you have (interlace, progresive. 4:3, 16:9). Once you have that, click on Filter and go to Misc, choose LOGO. Import your water mark logo as .png type file. You can adjust transparency by lowering number in Alpha Channel.
Export as MPEG video and save as .m2v file.
Import that into MuxMan (free) and add your audio there. It will create a .VOB type file which you can import to your project in Remake.
I am sure there are other ways to do this, but these are all free software.
You can do subtitles, but I do not think you can adjust transparency there.