From our point of view - anyone. From yours - please consult your local law, boss, parents or whatever.
Yes, you can delete your Account
Note that deleting an account is not equal to deleting Wikis. If you will delete an account, you Wiki will still be hosted by Wikidot.com.
Some of the problems related to session handling might be caused (and very often are) by strange configuration provided to you by your internet providers — such as routing problems, forcing caching, short dynamic IP lease time, filtering cookies etc.
If you experience any problems with your browser "logging you out randomly" — please try to experiment with the log-in options. In most cases this would help: