Seeing as though you seem to have little comprehension of the technologies employed to run your company network and that you seem to have very little trust in one of your key employees, you should maybe look into laying off your network admin and employing someone else. Go looking for someone with good, personal recommendations. Being a company owner you will probably have contacts of similar level and experience who could steer you in the right direction.
The other (easier and cheaper!) answer is to have a seperate PC/laptop in the office, dialup to the internet, independent of your network and keep it quiet. He can't look at what you've been doing if he doesn't know the machine exists or has no access to the machine.
THEN there's the whole email/server/internet question you tried to poise. ALL email will be routed via some kind of mail server. On a company network you probably have an email server and the mail is delivered to that, and then to your local email client (Outlook or whatever). Or, if you use an internet email account (AOL, Yahoo, whatever), the emails get delivered to their email server and then routed to your email client when you request them. I THINK this is what you are asking. Your english seems quite broken and I may noit have interpreted it very well. This question again flagged up your lack of trust in your network administrator.
Let me know what you think because I hate to think I've misinterpreted what you have said.