If a website has a domain name and within it contains another website name, is there infringement? For instance, is this bad: www.example.com and www.bestexample.com Or, what if the name contained the other website name but within one word: www.exam.com and www.example.com I assume that if the later example everything is ok, as its an entirely different name, but I am not so sure. Whats your opinion?
If the trademarked name is in the name no matter what order it is within the domain name is an infringement.
Unless the word/s within that domain name is being used as a trademark, no. And it's not just opinion. There are several decisions backing that up.
Lets see if the word Wii, Coke, World of Warcraft, XBOX, IPOD, IPHONE are all trademarked. What makes you guys think by putting words before or after those trademarked words would nullify the tradmark? This is an obvious answer to the question otherwise people would not continue to ask.
what about personal names? Let say soccer players? or si there a website where i could search if soemthing is trademark?
Personal names per se don't have trademark rights unless used in commerce. Using your example, soccer players don't have such unless, say, they sell or market certain products or services using their names over a period of time. One place to possibly search for trademarks is Google itself. It doesn't give an exhaustive search, though, especially since registration isn't required for TMs to exist.
I think the first one would be illegal if maybe it was a unique and registered name like "microsoft", if you used www.microsoftware.com or something along the lines of that, you would be in to some fines.