1) Ping?Pong! is not spam. This is the method used by a server to see if you are alive and responsive, i.e. to make sure that your connection isn't dead. If these messages annoy you, do the following:
[*] open mIRC
[*] go to the options menu or press Alt-O to open it
[*] go to the IRC/options submenu, and check the 'hide ping? pong! event' box.
2) It looks like your client's responses are not reaching the server. You, your school/employer or your ISP may have a firewall running that is blocking the replies, or you may be using an unusually badly configured mIRC script. If you use a personal firewall, check that the settings allow connections for mIRC, or for an appropriate port range.
3) Anyone can register a nick, they just have to be the first. I assume that the message to which you refer was an e-mail sent to your e-mail address. You obviously have the nick, and the password was sent to you... perhaps a kind friend just did you a favour? Or perhaps you just don't remember registering a long time ago? In any case, you can now go to the "My Home" section and CHANGE the password.
(I have had a different problem, where someone else has requested my password... it's no big deal, password info always goes to the e-mail address given by the original registerer).
4) If you are convinced that someone has broken into your computer, do the following:
[*] Download an up-to-date antivirus program, and run it.
[*] Run an online antivirus (because some viruses/trojans can stop the antiviruse on your own PC from working properly)
[*] Download an anti-trojan program like Pest Patrol
and run it.
[*] If you don't already have one, install a personal firewall like ZoneAlarm
to control incoming and outgoing connections. This will go a long way to preventing unauthorised use of your computer.
Hope this helps