Suppose I like some name and register it. Then I found that it was an established site before.. Could it create any problem ? Can the previous owner ask me to get his domain back ?
If it says "AVAILABLE" and you register it it's all yours. As long as there are no TM infringements, you are 100% in the clear.
TradeMark infringements.. Other meaning : The domain is belong to a trade mark name. E.G : www.google.com Trademark under USA trademark law
When a Domain name is expired, it would be on hold which allows the owner to restore the domain name to them. However when you are able to register the domain name, it would have already been release from the hold and treated like a brand new domain name. You can register it without any consequences since the owners does not want it anyways.
You should still check out the history of the domain, what it was used for etc. Check if its not "banned" from google.