Would 500 sit-ups be equal to 100 pushups

Sit ups and pushups work out different muscle groups, so no.

Be careful with traditional situps. I once temporarily injured my back doing too many far, far too quickly on a hard floor, albeit the only overly significant issue I can remember experiencing with them.

The main issue is that traditional situps actually work muscle groups besides your core such as hip flexors. That's not a problem in and of itself but one particular muscle group, iliopsoas, actually connects the pelvis to the lower spine and pulls on the spine when worked. This can be offset by stabilization muscles but traditional situps aren't an ideal position for this to happen in. If you're still going to do them, at least don't do them as quickly as possible. You'll not only get more out of them this way but you'll reduce the chance of hurting yourself.

But to answer your question, there's not really a solid equivalency between situps and pushups. I would venture to say most people who can do many pushups can do more than fives times that many situps, though.

Not at all, each work different muscles

500 situps would be equal to 500 situps.

You’ll destroy your spine doing situps and have to live with chronic back pain the rest of your life. The pushups are fine.

For calorie burn?