Time for a new door and springs. Do it before there's any possibility of your kids getting hurt if the mechanism or springs fail.

Gotta agree with Beverly. Keeping animals out is the least scary of many possible scenarios. I've seen springs snap and go flying. Can you imagine what kind of damage or injury that might do? And I've seen other terrifying mishaps with garage doors, all caused by lack of maintenance. You don't want to mess with this. Get a pro in to advise you a sap.

That's ASAP, not a sap. Sorry!

It's hard to be sure from just a photo, but the door appears to have a perfectly straight bottom edge. Could the gaps be due to the concrete not being level and/or flat?

As far as safety goes, you should definitely inspect your door and its mechanisms thoroughly, and get a pro to do this if you are not handy. OTOH, other than needing paint, and your concern about bowing, I don't see any obvious issues. (I'd tiewrap those cords to protect them.)

your concrete has settled. i have been putting in garage doors for years, and can definitely say that the problem is settling concrete.