If your email is sitting on a companies server they ability to read you email if they know your IP Address or now.
If someone has your IP Address and you have a firewall on your PC, or network then they would have no access to your computer. The exception to this would be if you had a virus on your machine which phoned home looking for commands to perform by the person who wrote the virus.
If you do not have a firewall installed on your computer or network then they could break into your computer.
As mentioned above, a firewall is important. You should consider upgrading your network class and then get a firewall. You can see your IP address by going to start>run>cmd>ipconfig.
It’s a lot more than just knowing the IP address. There is the issue of finding a service/application/port to gain access to the data/information or application. A firewall may block this access but it will not block access for authorized applications, services or users. So, if someone knows access credentials to the e-mail, they can gain access. If someone can gain access to the computer through an authorized running application which can be exploited to gain access to the e-mail, then the computer is no longer protected. One of the best summaries of computer security can be found in the article, 10 Immutable Laws of Security.