1)an extra minute of rest is not like taking weight off the bar. however, it's a lot like a good idea, because it may allow you to lift MORE weight. You'll get answers anywhere from 3-15 minutes of rest between sets, just based on the past posts I've seen on this topic. but really it's about making sure you A)can complete the next set, and B) do not cool down to the point where you need to warm up again.
2) you sound light.... to be a novice and be able to do that many chins makes me think you probably need to eat more, though I don't know your weight, height, athletic/training background, etc, so this is just speculation. That being said, just do 3 sets to failure and don't worry too much about failing on chins as your bodyweight fluctuates daily and believe it or not, adding 5lbs could cause you to miss a rep or two. Just be consistent.
also, post your stats