Yes. Trimming just removes junk data used to completely fill the game card. It doesn't remove the game data.
Yes. Because the size of the memory available to make a game is in divisions of memory, 1MB/2MB/4MB/8MB/16MB/32MB/64MB/128MB and 256MB, so if you want to make a game that is 37MB in size then you need to use a 64MB Rom to fit it all in. Anything over the 37MB's is padded out with rubbish that has nothing to do with the game you made. So yes people who make NDS games add garbage just to make up the space on the Rom.
I'm not sure exactly why they do it. Or if it's even the creators that do it, and not the nature of the DS Game ripping that just copies all the data, even the unused space.
Yes, they do, all Nintendo DS game cards do it. That is why every NDS ROM is a factor of 2 in size (like Prinnydood shows). It's not just a coincidence that every ROM is 16MB, 32MB, 64MB, 128MB, 256MB, etc. exactly. They are all padded to fill the game card size.
Compressed maybe, but uncompress them (extract) and do not trim them, they will be full size, a power of 2. (128 probably) By the way, Titen, did you try out the CycloDS 1.56 Beta 5? They added a new auto-patcher for the newest anti-piracy called "stealth mode", it seems that it helps out with quite a few of the problem ROMs.
They don't choose to do it, the data is automatically padded to the full capacity of the cartridge the ROM image is being written to.