Yes, the police do need a warrant to search your locked roof mounted cargo box.
yes, if you have a warrent out then they will search the vehicle.
Yes unless it's a car and the glovebox/trunk is locked. Premises includes all rooms
Regulations vary by state but they can search it with your permission, otherwise they can hold you until they get a search warrant
In general, the presence of a felon in a vehicle does not automatically give police the right to search the vehicle. However, if there is reasonable suspicion that a crime has been committed or that evidence related to a crime is present in the vehicle, police may be able to search it, depending on the specific circumstances and applicable laws. It is important to consult with a legal professional for advice tailored to your specific situation.
the 3rd
Yes.
Yes, if they have probable cause.
As with any other vehicle, it'll require probable cause. If a police officer sees a lot lizard go into your truck, for example, then they have probable cause to search that vehicle.
A police officer must have either your consent, a warrent, or probable cause to search your vehicle - probable cause to search can include everything from a partially hidden weapon (gun), blood, body parts to just the cap of a alcohol container sticking up from a seat.
In certain situations, YES.
You have every right to say no.