Arrest warrant?

An arrest warrant only gives the police right to enter if it is the subject of the warrant's residence. An arrest warrant doesn't give the police right to enter the residence of a third party. 

SO, if by "stays at his parents' house" you mean that he is only staying their temporarily but resides elsewhere, the police may not enter based on the arrest warrant. The police may weight outside until he comes out or they obtain a warrant from a judge to search the residence for him.  HOWEVER, if by "stays at his parents' house" you mean that's where he's living, meaning he has no other permanent address, then his staying their establishes him as a resident and that as his residence, so the police can enter, regardless of whether or not their address is listed on the warrant.

All of that said, when the police are standing on one's doorstep, say they have an arrest warrant for him, and ask if he's there, if one says no but he is, one is committing a crime, and if one say yes, the police will generally say something like, "We wish to enter your home at this time to execute our warrant. May we enter?" and unless one expressly says no, which people rarely have the fortitude to do, the police come in with the permission of a resident of the home. 

Yes.  If the cops have a warrant, they can charge people with obstruction if they try to prevent the cops from getting that person. 

Hide him in the basement