What is the name of a legal method to obtain evidence by examining a person's home, vehicle, or business?

seems a bit mean that, just because someone suspects you of doing something wrong, they have the right to invade your home and your privacy

In the UK, you need a Warrant.

It's by a preponderance of evidence (very strong) that evidence will be lost very soon if search is delayed. It's not just a guessing game. When done properly, it can often result in very bad acts from happening