For the 1st question... My understanding is that Windows remember how the browser was closed last time, and will reopen it to the same size. I suspect that all of your pop ups caused this issue. If the pop ups are small, and they're the last one to be closed, then the next time you open IE, it'll remain very small. I had seen that happen. See solution below.
For the 2nd question, you probably should download some scanning software to scan and clean up your cookies, spyware and 'bad files' that caused the pop-ups. A good free one is Ad-aware. Free to download from
http://www.lavasoftusa.com. This is not a virus scan software. Run this regularly and remove all junk files on your PC. After that, the pop ups should be gone.
Also delete all cookies and cache from IE. Go to TOOLS / Internet Options. Click on DELETE FILES and DELETE COOKIEs.
If it still comes up, check your startup folder on your C drive. (Do a search on startup folder) Remove anything that looks like porn related. If you're not sure, move them out to the temp folder first, and delete them afterwards. Also check your registry key for the RUN value (This one may be dangerous if you don't know what you're doing).
You should also get firewall to protect your PC from being attacked and flood by all these junk. This one is easy to use, free also.
http://www.zonelabs.com/store/content/home.jsp.
Hope this help.