I think it would be better if you removed the picture from your tag. Not only due to size, but some people may also mistake it for being part of the sheet. That said, it's not especially against the rules or anything, it's mostly just preference, so just do what you think is best.
As for the background, generally a sheet should have a coloured background, something that contrasts well and is unused in the sheet itself is best.
Magenta (#FF00FF) is popular, but it can be anything that fits the bill really; redblueyellow often uses
#008080, and usually use
#00AE00, so it doesn't matter a great deal. Black and white are greatly discouraged, both because they're often used in the sprites themselves, and also just because they aren't very easy on the eyes. Transparent shouldn't be used unless you have anti-aliased or partly-transparent sprites, i.e. they contain pixels that aren't ripped at 100% opacity.
However, in your specific case, you do have a point for using black, at least with the NPCs. Even though the black is technically transparent, the sprites are made to be viewed against a black background. This is actually similar to the in-game battle sprites for
Pokemon R/B; the white parts are actually transparent, against a white background. The difference is, Pokemon outlines the sprites in black or grey, so they can be separated from the background (and put against magenta in the sheet), while these sprites cannot since their outline is actually part of the background. You could try and estimate the outline yourself, but I personally think that could compromise the accuracy of the sprites. I think that using black is fine; it's what I did for
these sprites, since I also couldn't rip them without the black background.
I'd say the same goes for the Willow sheet; again, if he only ever fades to black in-game, you can't rip it otherwise so that's how it should be sheeted. However, if he doesn't have outlines like NPCs, and you can clearly see what bits are and aren't supposed to be transparent, then maybe you should only give that single animation a black background. That is, just isolate the walking animation with a black background while giving the rest of the sheet a different coloured background.
By the way, just for future reference, it's always best if you don't scale down sheets when asking for help or suggestions, we need to be able to see all the pixels properly to give proper feedback (e.g. I couldn't properly see Willow's sprites). If they're a bit big to embed you can put them in a spoiler or just link to them.