Yes, you can link from one site to another.
I would suggest, though, that it's a bad idea, especially for a newbie such as you describe yourself. It makes a lot more sense to put everything on one server.
There are a lot of good ways to set up servers, and consequently, it's very likely that a newbie - or even a highly experienced pro - will get confused.
Additionally, by putting everything on one server, you won't confuse users by having different domain names.
It can be a little easier to register your domain name through your hosting company, because the nameserver information is already plugged in for you, but it's not exactly rocket science. If you can't type in the names and IP addresses of the name servers (and with many registrars, you don't even have to type in the IPs, because they look them up for you), then you probably can't handle the hard parts of building and running a website, either.
Some registrars are easier to work with than others. It's sometimes valuable to be able to switch registrars without worrying about alienating your hosting company.