Hiya Sands,
Made it out of the sandbox and am relaxing in California... finally got access. As this stuff is what I do, here is my 2 bits.
As pointed out, good anti virus and firewall (from different vendors, not the same!) will do a lot to help. Common sense is also a BIG help.
To your questions!:
1. How much can you see in someone else's computer?
Everything is possible. I routinely repaired my fathers PC in the US from the middle east. This included watching as he "showed" me waht he was doing and problems he had, controlling <his> mouse and menus etc.
In short, if someone gets in, they can see everything. Hint-don't let them in in the first place.
2. If you delete/change a password, is it all really in the registry (yahoo, for example). If you save the passwords, they are on your system. IE and Firefox/Thunderbird/Outlook all offer an option to encrypt the passwords. I use this on this system I am typing on now with Firefox and Thunderbird. I have a "password file"that has all the passwords. When I start up, I 'open' this to the software to use. When I go to deeper blue, it takes my password for the site and enters it... makes it easier. I consider this an acceptable risk. I DO NOT STORE MY BANK PASSWORDS OR USER NAMES. These I type in manually and do not let be saved.
3. Can somebody else access your computer without your knowledge, and watch what you are typing?
Short answer, yes. See above, item 1
**NOTE that in your specific area, IT staff are NOTORIOUS for doing this, especially to women. I caught many IT Staff doing this there, especially to females. I found it a bit freaky.
4. If you connect your laptop to a LAN line, and download emails to Thunderbird/Outlook, is it true that the "IT WHIZZ" can view the headers (or even the whole body) of those emails?
Answer-Yes and no. Yours yes most likely, mine not. This is a setting issue. Mail normally travels insecurely by default. I for example, can see my fathers email being sent out the internet line I am using right now... every word, his login name, password, the works. (he is not using Yahoo/Hotmail, these encrypt the logins... somewhat) Your email client, Thunderbird, supports secure email which encrypts the transmission between your computer (e.g.; laptop) and the mail server if the server supports it. If your using Thunderbird with a pop or imap account, go to the settings for the account, click "server settings" and try clicking on the ssl. save exit, restart and try to see if it still works. You may have to accept a certificate. There are also TLS options which is security done a bit different. It all depends on what your server supports.
If using Hotmail etc with their encrytion, always select the secure option!
HOW MUCH CAN THEY SEE
all

In the end, the truth is that all major countries can crack through the stuff I mention, even at near real time. Hackers, script kiddies, and the like including the IT folks in your country (and at your ISP most likely) play around and watch people for various reasons (my professional 16 years of security experience and 3 years in your region speaking here)
What can/should you do?
1. Always keep your system updated and patched.
2. Run a firewall and antivirus (from different not the same vendors)
*If norton has a vulnerability like recently and you have all your security based on norton, you have a problem until they fix it.)
3. Use high security settings, set your options to higher security in your browser, mail clients etc.
4. Don't blindly open attachements!
5. Backup your important files and mail regulary!!!!!!!! I will say that again, Backup your important files and mail regulary!!!!!!!! I am comfortable if my system is wiped out <right now> and can have it up by morning...
6. Change your passwords regulary (every couple of months) or if you think someone knows your password. Make sure you change it securely!! Use non-words. My last job I found 89% of 1500+ peoples passwords were easy to break (easy as in 20 minutes on a 486) Example of a "good" password that is harder to crack : 1H4rDp45sw0d Note no repeating characters and a good mix. No "real"words. 1 hard password. Pick one that roles easily off the fingers when typing though-that one is not easy to type! After a few tries, you will be able to type it fast. Also, use a separate password for your bank account and for your work account...
darn... I types a bit too much. Oh well, I am a security nut so oh well. Some may argue with my recommendations and thats fine but these are some good general practises that will stop 90% of your problems.