vary from town to town, but it's very rare to be held for more than a day while you are arraigned.  I've heard of some places that let you go after you are booked and sometimes you just pay a fine and are on you way.

The best way to find out is to consult a lawyer in your area.

As far as who LE are, they are the guys in blue uniforms riding around in shiny cars with lights and sirens.  Try to keep a distance between you and them.

(still not a lawyer)

All states have some form of solicitation laws which usually in stings.  Its been my experience that LE or Vice only target "street prostitution"  because its visable.  Sometime you may read about hotel bust where many prostitutes frequent.  Some jursidiction look at agencies like in the DC Madam case, why ?  Other than to discourage form of organized crime being linked to  prostitution like gun running, gambling, etc

AS stated LE goes after the visible, usually in response to complaints.  Street prostitution is VERY visible.  CL is VERY visible.  If providers & clients are not discrete, can bring complaints about hotels...  
I'm convinced that very many hotels know what is going on but the boost to occupancy rate is too good to pass up...  but NO hotel would have any choice but to cooperate if complaints are made.  

Read up...  Learn to be discrete.  2 call system you call from your car at exactly the time specified.  Be discrete with your calls.  In an urban setting, if you must call from a lobby window shop or something so as not to be over heard.  

Learn to blend in.  Do not carry gifts openly through the lobby.

Act like you belong & know where you're going.  Ladies, if a front entrance is used, give the gents directions to the elavators.  "Through the lobby & to the left...  Rm xyz"

Everyone being discrete is what counts.
skb

having sex for money isn't.

You have to get married to have sex for money legally.