It's approximately a 1980+- DS100. Search google images and you will find some that match up.
As for running backwards, many two strokes will under the right circumstances.
It may be something like the woodruff key holding the flywheel in alignment has sheared. This will mess up your timing. Or it could have been improperly set. Or the timing is fine and it just happened as a freak occurrance when the bike kicked back on you.
Not positive re: anything on a DS100, but there should be a cover over the flywheel on the left hand side, lower portion of the motor. Remove that and take a look for any timing marks. In most cases, you will have to remove the flywheel to check and adjust the timing. Flywheel removal may require a special puller. The manual will tell you about that part.