gmail not filtering spam and other problems

1. My gmail has stopped filtering out spam. Multiple messages now appear in my "All mail box" and/or "Important." I have made "delete" rules in preferences but they don't work.
2. All mail is sent to "All Mail" instead of to individual mailboxes, despite rules in preferences (which worked until recently).
3. Messages do not come to the Inbox, but to "Important" or "All mail."
4. Messages left in the inbox suddenly disappear, often completely,: they aren't in the "All Mail" or "Important" mailboxes anymore.
5. Mail indicates new messages when there aren't any. A number will appear next to a mailbox, indicating new mal, but there isn't any.

Do I have to replace the program completely somehow? Delete its system preferences? If so, how?