A modestly out of true wheel isn't likely to be a real safety concern, but I'd be concerned that if an entire section of the rim was so bent to cause a whole section of spokes to go slack, that you may actually have an increased chance of lateral failure and a crash. Also if you are riding without a rear brake if anything happens to your front brake you're completely screwed. Your bike sounds like a death trap. I know new bike availability is terrible right now, but maybe try to look for a used bike in the extremely near future.