Can I use a domain if the name (not the domain) already exists but it's not a trademark? For example, if there is an established and popular website called "The Best Portal" (ONLY AN EXAMPLE) but they don't have their own domain, their site is hosted on a free server. Can I purchase the domain thebestportal.com if it is available and not have any problems with them? *Again, that's only an EXAMPLE, I have no idea if that site really exists.
It is going to depend on the exact term, not an example. If it is a term able to be trademarked, then the other parties first usage in commerce gives them automatic common law trademark rights for that usage - they don't need to do a registration to have trademark rights. It doesn't matter if they have a domain.