I have some tomatoes that have split on the vine. Can I leave these and
will they "heal" and continue growing or should I remove them now?

Also, now this may sound crazy, I've gotten an old blender and I've been
rendering down all my peels to soup for my compost. Basically anything
like melon rinds, banana peels egg shells, etc..... Is there any kind of
"soup" recipe I should be mixing for my compost or could I pour this
sludge right in the garden? I've also been juicing carrots and have all
the left-over from the scrapings. Is that better in the compost or garden?

Quoting embertr:
I have some tomatoes that have split on the vine. Can I leave these and
will they "heal" and continue growing or should I remove them now?

Depends. If the cracks are rather large -and- the fruit has already
started to blush, personally, I'd pick it.

If you're expecting a rain or need to water, pick 'em if they've
started to blush, even if the cracks are small.

A tomato ripens from the inside out. Just put them on your counter
out of direct light to finish up (not in a sunny window - that's a
myth) and they'll be just fine.

If you've got total greenies, best to leave them on the vine and take
your chances though.

Also, now this may sound crazy, I've gotten an old blender and I've been
rendering down all my peels to soup for my compost. Basically anything
like melon rinds, banana peels egg shells, etc..... Is there any kind of
"soup" recipe I should be mixing for my compost or could I pour this
sludge right in the garden? I've also been juicing carrots and have all
the left-over from the scrapings. Is that better in the compost or garden?

Again, depends. Most of what you've listed is a 'green' (nitrogen
source). Personally, I find it a lot easier to come up with 'browns'
than 'greens', so I'd want those items for the pile.