Can my modem be modem and router combined in one unit? Installed by internet company?

Yes Modem/Routers are a thing and there are many of them. If they are providing you with a router then it likely is a Modem/Router. 

I'm not sure what your asking, but you can use your own router though it would require putting their modem Router in bridge mode (disabling the router part) and setting up IP Passthrough so your router controls everything.

But unless you know what your doing or have someone close to you that does, you may want to just use their equipment as most providers will only provide so much assistance when you ask to bridge mode their devices.

If your having trouble connecting the router provided to you call your provider. It's their job to walk you through setup/installation or have a tech come by and install for you. Remember your provider will only help when it come to there equipment in use, any third party equipment (anything not provider by them) they will not support.

There is a lot that can go wrong if a mistake is made, so I only recomand doing what you fill comfortable doing, as well as comfortable fixing if something goes wrong.