One of the primary reasons fans wobble is due to loose connections. If you are planning on installing a new fan any time in the near future, make sure you tighten all of those screws completely. Doing so will prevent you from visiting this page again!
As a kid popcorn was such a joy. Now that you own your home and have it on every ceiling in the house, not so much.
Has it been painted? If you popcorn ceiling has been painted previously it will be more difficult to remove it. The reason for this is the process to remove it is literally just wetting it down and scraping it off. If it has been painted one or more times, the water won't be able to penetrate the paint and unfortunately, you might just need to have it done professionally.