Ratings got higher

I have noticed while my rating skyrocketed from 1200 to 1500 my skills did not improve and opponents with ratings over 1400 got significantly weaker.

I generally play 10min live chess. Anyone else noticed something similar? Or maybe chess.com rating system changed somehow?

I wouldn't call that skyrocketing. It's looks like a slow and steady progress. It's just possible you've gotten better.

That's just how it feels when you get better at the game. you notice mistakes in your opponents play more often because you've been playing longer and you're been in those situations before. it's harder to notice your own mistakes because you don't make the same mistakes anymore. it's totally natural and it happens in any game you'll ever play.

Sort of building on the same idea, what is a reasonable amount for someone's rating to rise if they play everyday? 

My standard rating has risen from 1559 to 1623 in 7 days, and from 1449 to 1623 in 30 days. Are these jumps in rating high/low/average?

I don't have any statistics but I would guess that your 600 point ratings increase in the last six months is far above average. 

Thanks for the replies guys!