In answering your question, I'm assuming that a "surveillance officer" is someone who is assigned to ensure that people on house arrest or court supervision are complying with court orders, and that a "home checkup" is a visit to enforce compliance. That said, if a condition of the house arrest or supervision was that the person under supervision was not to consume alcohol, then, yes, the surveillance officer could administer such a test.
The police would never show up and demand a breathalyser. If you were of legal drinking age there would be no purpose to do so. If you are underage you can simply tell them to leave and you can deny the breathalyser. That can't bust down your door and demand a breathalyser.
Yes. Unless you invite them in, they have no right to come into your home regardless of what it is.
yes
Most have a gun locker at home.
YES
Police officer with a search warrant can search any home regardless of the situation.
If you're on probation then they have the right to enter your home. Also if they have a search warrent.
(in the US) Some departments have such a 'take-home-car' program but, because of the cost, the majority do not.
Yes, if they are in "fresh pursuit" of the individual.
Police officers are trained to use an open hand search when they are searching somebody for weapons. To enter the home, the police need to have a search warrant or the consent of the owner.
In order to search through someone's home, police officers must aqquire a search warrant, which is just a slip or piece of paper signed by a judge that gives them legal rights to go searching through a person's home. They also must have some sort of evidence on why they are to search someone's home, such as drugs, leads, etc.
Police officers generally do not provide citizens with rides home unless there is a specific reason to do so, such as ensuring the safety of an individual who is unable to get home safely on their own due to intoxication or other factors. This is done to prevent potential harm or accidents. However, policies may vary depending on jurisdiction.
If he's giving you a ride home, yes, the officer can keep you in handcuffs until the interaction is over. Police officers are expected to provide for their own safety.