Can I register a trademark that has already been registered in another country by someone else?
Trademarks are territorial. For example, if a company uses the trademark in Europe, it has no rights and protection in the US. The registration of the mark in Europe does not extend to the US. Therefore, the fact that European company has and uses the mark in the EU is not relevant at all for the registration in the US. You should have it in mind when registering your brand. If you are operating in more than one jurisdiction, your mark also should be protected in all the countries where you use it.
In most countries, the trademark must be used to be valid and registered. The registration owner must file required maintenance documents at regular intervals at the US patent and trademark office or pay renewal fees in Europe. Failure to file the required maintenance documents during the specified time periods, or failure to pay the renewal fees, will result in the cancellation of the trademark registration or invalidation of the extension of protection. You can watch this US PTO, that explains the issue. In Europe, if a trademark is not used for the last five years, you can cancel the registration of the mark and also register it newly. Therefore, if you see in the trademark databases, that the mark is no longer registered (can be canceled or abandoned) or is no longer in use, it means that nobody has any more rights of this mark and you can register it.