The answer is yes. You are roomates, not just housemates. Your roomate could hide a weapon or drug under your clothes. Even if you were just housemates, the police could probably check every room, too.
Did they find anything in your room? That's when the Fourth Amendment and the analysis of your rights vs your roommate's, probation vs a new search, would be triggered. Short of their finding anything in your room, you've got no recourse and the best thing to do might be to find a roommate who's not on probation. Your roommate's probation conditions leave him/her with a drastically reduced expectation of privacy - basically, he has none in the eyes of the law - so searches like this can take place as often as Probation wants, as long as they're not solely for the purpose of harassment. Again, though, unless there's something they found in your room, let it go.
Yes, and because the are searching for contraband. It doesn't have to be actual possession it can be constructive possession, so if they find contraband in your underwear he's screwed.
The response above is not intended as legal advice since it’s impracticable to provide thorough, accurate advice based upon the query without additional details. It is highly recommended that one should seek advice from a criminal defense attorney licensed in your jurisdiction by setting up a confidential meeting. Moreover, this response does not constitute the creation of an attorney-client relationship since this message is not a confidential communication because it was posted on a public website, thereby publicly disclosing the information, which is another reason to setup a confidential meeting with an attorney.
Technically, they don't have a right to search your room if your room is not a common area, is not utilized or shared with the probationer and you have exclusive authority over your room. But, whether an officer will comply with this legal requirement is another issue. I often tell clients who are on probation and live with others who are not on probation to identify their room and belongings by placing a sign on the outside of the door. In other words, you can put a sign outside your door that says, "Jeff's room". As long as your room is not a commonly shared area, then you have privacy privileges. The other thing you can do is find roommates that don't have search and seizure terms and conditions so that you can enjoy peace and quiet in your place of habitat.