Converting videos in the background using automator and handbrake
First, I'm assuming that you accidentally chopped the '/' character off the front of the path to Handbrake in your example. Second, when you say "hidden mode" you mean run in the background.

What happens if you run the command from the command line?

How do you know the command isn't running when you run it in background mode? Are you doing a "ps" command from the command line to see if it is running or not?

Have you tried adding ">>~/HB_log.txt 2>&amp;1" just before the "&amp;" command so that you get a log of both the output and the errors it might be putting out?

If only the first part of the name is being used then I assume that the quote characters around the name are being stripped - try escaping them with a '\'. Like so '\"/Users/abc/Desktop/TestVidDest/$(basename $f)\" ' and see what happens. 

I also suspect that problems with the name might be upsetting the entire line and causing your problem. 

I would actually write a shell script that you could test externally and then call your shell script from Automator.