Let's say you wanted to use something like googling.com or amazon-fun.com (examples), would there be risk or problems that you know of for copyright infringment?
I had one of a trademarked name like like word1-word2.ca and I received a cease and desist letter from their legal council, so shut it down and had to transfer domain over to them. I'd get some legal advice or you'd may risk what happened to me.
I seem to have had some domain names taken from me by euro id. No letter no warning, just refusal to renew
Having a trademark in a URL does not automatically mean that you would lose the site if it were contested. Of your two examples, you would almost certainly lose googling.com no matter what content you put on the site. When a trademark is a made-up word, protecting it is much easier. The amazon-fun.com would be the type of domain name that it would depend on what you did with the site. If, for example, you were to put content up that dealt with chartering tours of the Amazon River or a blog that talked about South American deforestation, then you would stand a good chance to keep the site in a dispute. If, however, you made a site about what a person can do or find on amazon.com then it is much more likely that you would lose the site in a dispute (as this could be seen as causing confusion, using another's trademark for your own benefit, etc...). If you merely parked the domain, you would also be very likely to lose the domain in a dispute as that would be seen as having no legitimate reason to use that name. But it doesn't stop there. Even if your domain and site fell under generally accepted uses, both the courts and ICANN look beyond the one site. They will look at all of the domains you own. If you have multiple domains that contain trademarks that will be seen as evidence of bad faith registration.