I'll assume you meant to ask "Can the police search mycar when I'm not there?"
The only situation where the police would require your presence is if the justification for the search was your consent. Otherwise, the search could be based on the car appearing to be abandoned, unlawfully parked (which would permit it to be towed and inventoried), used in a crime, based on probable cause, incidental to an arrest, or other other circumstances. Even a consent search would be lawful if you or someone else having control of the vehicle had given their consent for a search with you not present.
Yes
Yes they can search it
yes, it is not considered a "search"
no
If they have probable cause.
I think they only can search the car if they have probable cause.
Police are liable for the damage that they do to your car. You can file for damages against the police department to get your money.
I think that would be rather difficult for you to search your car while in handcuffs. Now, can the police search your car while you are handcuffed? Sure if they have your permission or if they have a search warrant.
Prowl is what they do, not what they are. To go about stealthily in search of prey
The vehicle can be searched with probable cause, or if the car is being impounded an inventory will be done. The police do sometimes ask for permission as well, and that is another way the search can be valid.
The fourth amendment protects citizens from an unreasonable search of your car.
NO they can not unless there has been a warrant to do so.