Can a police office enter a home of a citizen to search for 3rd party with an arrest warrant of the 3rd party?

If there's probable cause to believe said third party is there, yes, absolutely. Warrants don't get issued unless there's probable cause. Judges don't just toss them out like candy. The police have to have a good faith belief that said 3rd party is there, and the police must show why they have said good faith belief; and it must all pass constitutional muster. Hope that helps.

If the police officer has reasonable belief the individual may be in that person's home, they can search the home for that individual. If this wasn't the case, the suspect with the warrant would just go to a friend's house and hideout. There is no safe haven for a person with an arrest warrant.

Yes, so long as they have "probable cause" to believe that he can be found there. Here.... http://mjpetro.typepad.com/7th_circuit_alert/2009/09/police-need-probable-cause-to-execute-an-arrest-warrant-in-third-parties-home-.html is a good discussion of a recent case from the 7th Circuit asking what threshold of probable cause is needed. Richard

Yes, if they have probable cause.