Remote control and screenviewing on OS X?
This isn't exactly true. They can see the sites you visit but not what the content is if you're using HTTPS. This means that they can see you're checking your balance but not what your balance is.

This also applies to company network traffic providing they're not doing MITM which they can't do without inserting their own certificate on your computer. I suggest checking the certificates installed on your machine in Keychain Access to see if there's a certificate installed.
You can disable these to disable the relevant services from being accessed through the methods detailed in the information shown by clicking on each service. Disabling these won't prevent against third-party software installed on the machine providing similar functionality.
Any third-party software could provide functionality such as remote access. I'm unfamiliar with this specific software but it may be a good idea to research exactly what specific software installed on your machine can do.
You can re-enable the firewall, however be careful that this does not block any legitimate traffic that may be required by your work network.