I cannot drop or remove the boots of springheel jack, i have completed the TG.

When I wear them, y does my character become slower? I wear full heavy and am an expert at HA. I think it's because I no longer have the full set of heavy, confirmation would be appreciated.

And last but not least, messing around with the gray fox cowl, killed 3 guards and hit 2 civilians, whilst the battle music was on I ran to armand and removed bounty but the guard kept chasing and I've left the IC altogether now and entered a cave but battle music won't stop! I know it's probably a glitch, my fault I suppose, I just thought once you remove the cowl all the bounty would go away, but it didn't, :S

Aren't those boots Light Armor? What's your light armor skill level?
You have to be safe, no battle music, then remove the cowl.
Yes, sometimes those pesky guards keep coming. Once, after a certain Daedric quest, I actually had to run into the water near Bravil, and using Alteration, stay at the bottom of the channel until the guards drowned. Battle music over, I swam to shore.

It's finally gone now the music, it was a guard in the thieves guild hall! Once I killed him the music stopped, bit gutted because now I have 14 murders because a little fiasco with the cowl!

The boots aren't light or heavy it doesn't say, bit yeah when equipped my character becomes much much slower, as I said he wears full heavy.

And also I've completed TG and cannot drop them or remove them, same as the big heist plan scroll.

If you're on PC, there might be a solution. For me, it would be to reload the save before you had issues. I have auto saves off, so I'm especially fanatical and OCD about my saves.