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You can't do it with this amp.  If you're playing live, have a 2nd guitar set up at the lower tuning.  Or leave your guitar tuned lower, and use a capo for the 'regular' songs

Are you sure this was 'gain' and not just an increase in volume?  The master volume setting is not saved with patches, only the channel volume.

There 16 banks of 4 patch locations each available as User Patches, so 64 total stored patches.   Yes, you can access them and save them from the front panel of the amp.  Suggest you read through the Advanced Guide:    http://line6.com/support/manuals/spideriv75

The Express allows you to switch between the 4 active preset locations in the amp, A,B, C or D.

The easiest way to do this is to plug the output of the HD300 into the CD/MP3 input on the back of the Spider amp.  This bypasses all the preamp circuitry of the amp.

The Spider IV 15 (and 30) does not have a distortion FX. If the 'drive' control does ntodo anything (try all 4 presets), you can first try a factory reset - hold the 'A' button in while turning on the poower, kep it held in for 5-10 seconds.   If that doesn't fix it, then you should return the amp to the place you bought it for repleacement (15s can't be repaired).

The headphone/DI output (that's what I assume you are trying to use) is not amplified - you can't use it to drive a cabinet, you would need to send that signal to an amp first.

Step on the toe (very hard) of the pedal, and it will switch between WAH and VOLUME operation.

Yes, but the amp only provides audio ouput (from the DI/headphone ouput jack).  You would use this stereo audio output into an appropriate audio interface (Line 6 UX2, for example).  You could try adapting to the line-in of your computer, but typically the OEM sound cards in computers are not suitable for audio recording/reproduction.

First, back them all up to your computer, using Spider Edit.  Then you can move any/all around to the User Preset locations.
Without using Spider Edit, select the preset you want, then save it to the new location where you want it.

That would be my guess.  Hopefully your amp is still under warranty, as the 15 is not servicable.

First uninstall Monkey on your computer.  This includes deleting all files in the 'Line 6' folder.
Then download and reinstall Monkey.
Connect your Shortboard only (do not connect the amp to it) and use Monkey to update it.  Then connect the amp to the Shortboard and see if you can get Monkey to install updates.
If not, you can start a repair ticket on this site, but your best bet will be to call the Line 6 support line.

Arachnobia has that setting - the pedal is for pitch glide.   You need to go into the patch settings, turn off pitchglide, turn on a wah style, and save this patch.

Push and hold the 'A' or 'Clean' preset button while turning on the amp and hold for 5-8 seconds.  This will perform a factory reset.

The only way to use VSTs not provided by Line 6 would be to insert them on tracks in a DAW (recording software).  Unfortunately, this makes it difficult to insert an effect into the chain in PodFarm (you may need to run two instances of PodFarm as inserted VSTs in your DAW, with the non-Line 6 VST inserted between the two.

You don't want a MIDI interface - MIDI is data, not sound.
 
What you need is a good audio interface.  M Audio, Tascam, Steinberg, many choices depending on your budget.  I recommend someting with at least 2 channel capability and 2 line inputs, this way you can take the stereo DI/line-out from your Spider to a splitter and put one channel (left) into one input and the other channel (right) into the second input and record them on separate tracks.