Check your state Constitution, and any other applicable laws regarding "search and seizure".
Our Fed Constitution requires a warrant describing places to be searched and items to be seized. And it needs to be pretty specific.
As to the condition they leave your property in, after the search that's going to depend on who is doing the searching and what their governing authority will let them get away with.
You might get lucky enough that the cops will behave look around the obvious places and some of the less obvious and not trash the place in the process. Wouldn't count on that, but one can hope.
Oher end of the spectrum is they will tear everything apart, find nothing, then just leave. They can, and have done that.
Your only real option is to fully document (video, especially) the condition of your property before (like now) and what they leave after the search. THEN submit that as evidence in your lawsuit for damages and compensation.
I know of one case (though it was back during the Clinton years, IIRC) where the ATF "searched" a house when the owner wasn't home, looking for (illegal) machine guns. They had a warrant, of course.
They broke the front door off the hinges, trashed the house, cut open the gun safe, pulled all the guns out and, finding no machine guns, left them lying in a pile on the floor, and walked away, leaving a note that said "nothing taken ATF".
Neighbors kept an eye on the place until the owner was able to replace his front door. The extreme end of the range is cases like this, they can tear up, break and destroy your stuff "searching" for illegal items. They don't HAVE to be nice, or careful and they don't have to fix anything they break. It doesn't seem right, but they can do that, and you need to sue (and win) to recover damage compensation.
IF their search was fruitless, generally you will win compensation...at some point down the road
The only persoanl expirence I have with my place being searched was a couple decades ago, Sherrif deputies, looking for my wife's brother. They didn't have a warrant, and they politely asked if they could look around. Wife's brother wasn't there, we told them, but did allow them to look around. They were polite, respectful, looked in rooms and a couple of closets large enough to hide someone in.
When one of them started to open a dresser drawer, the other one stopped him, and said, "the guy we're looking for weighs 300 pounds, he's NOT going to be in a dresser drawer!" The other one, stopped and said "oh, ...right", sorry... and then they left.
I wouldn't count on that level of respect or professionalism today. I'd like to see it, but I wouldn't count on it.