5.25" floppies won't mount

By default, the floppy kernel module is not loaded. To load the module, invoke

sudo modprobe -v floppy

Remember to add your user to the "floppy" group; to do that use

sudo adduser $USER floppy

After the module is loaded you should be able to access the hardware and mount floppies.

I did some research about Varian files, and I came up with this. Said something about a custom 5 1/4" format for disks, customized BIOS routines - I skimmed it. Sounds like it runs from DOS, so maybe it'll work from DOSBOX? Here you go:
http://nmr.tamu.edu/vhelper.php
Re-reading it a bit, the last class of computer that they say it reliably works with is a 486 and almost not at all with Windows. If all else fails, at least you have some EXEs you can work backwards from to potentially determine the format. Here's hoping there's not a whole lot of BIOS patching going on. If you need to attack the Pascal EXE, you'll want to UnLzExe/Upack/Uncompress it before you toss it into your decompiler. Program files from that era are almost always compressed in some fashion. Good luck.

Older Updates

Got a lot of tips for you here:

Most motherboards these days have the floppy controller turned off, have you verified that it is turned on?

Also, turn on the option for a floppy drive seek. If it doesn't seek, you have a problem of some type.

Let see, what else... if the connector looks like a Nintendo NES cartridge connector, it is more likely a low density drive (360kiB). If it looks like the old PATA connectors, then it is more likely the 1.2 MiB high density disks. You won't be able to read HD disks in a standard 360k drive.

Oh, also, if the light is amber or green the entire time you turn on your computer, the cable is plugged in upside down. Flip that bad boy over, and you'll be good to go.

And finally, if this is a Apple / Commodore / Atari branded floppy, you have to have a special card to make it work with an IBM PC. And you will surely NOT be able to read those style disks in an IBM PC drive. Their sectors, clusters and maybe even initial head positions are in different places. I've heard of 3rd party cards that will allow a PC to interface with the drives, but I don't recall what they are.

More info is good. Please share what brand/make/model of floppy you are trying to use, and what your motherboard make/model is.

Edit: Earned a downvote because the question changed, and I didn't change my answer fast enough. Or it's formatted like crap. Fair enough.

Updated Answer

Did you say those had 13 sectors per track? Wonder what kind of disks those are? Research says that they are likely Apple ][ floppies; I don't believe you can read those with a native IBM PC floppy controller. They could also be C64 or Atari disks
This isn't the one I remember, but it may help you out: http://www.deviceside.com/fc5025.html
Note: It says it cannot help you read "flippy" disks without an Apple/C64/Atari drives.

GNU ddrescue

Oh, I see that you are using ddrescue. Last version I used was 1.14, I can't imagine 1.16 is too different. Remember use -c15 for 5.25 QD, and -c18 for 3.5 HD.

Quick Rip, not using direct access. Log will help you remember that it is all good:

sudo ddrescue -Bv -c15 /dev/fd0 floppy.img floppy.img.log

If the disk has bad spots, skip them. Use log for just hitting bad spots next time

sudo ddrescue -Bndv -c15 /dev/fd0 badfloppy.img badfloppy.img.log

If you need to get down and dirty and work around bad sectors, this splits and retries 5 times.

sudo ddrescue -Bd -c15 -r5 /dev/fd0 bf2.img bf2.img.log

Mounting images

That is something I can answer!

To (hopefully) determine fs type:

file -Ls floppy.img

OR

file -Ls /dev/fd0

Now, once you can mount it loopback.

mount -t msdos -o loop floppy.img /mnt/floppy

If it does manage to be one of those pesky HPFS disks, you may be able to use fdisk to determine the offset to mount the hpfs partition, because what you can initially see is just the HPFS FAT-equivalent. I've used it for hard disks before, it shouldn't be that different. Update your question, and I'll return and (hopefully) answer it.

If they're in DOS format, you probably want to use the tools from the mtools package rather than trying to mount it.

Install the mtools package from the archive, and then use "mdir", "mcopy", etc. to access the files.