It's my understanding that it is NOT illegal for websites to post ads etc of ladies of the night And Websites such as TER and Other known sites are still  free to do so without having to worry about prosecution.  The problem is these Sites Are Worried That They Are Unable To Police Themselves.  In other word they don't spend the money to ensure that all ads and posts are legitimate from individuals who are of Legal Age.  
Fosta-Sesta  enables lawsuits against sites that allow ads for Sex Traffic Individuals whether or not they were aware or not.   It puts the burden on the Site to Insure that this is not occurring and these sites don't have the resources to do so.  
If I'm incorrect in my analysis please advise  
https://en.wikipedia.org/wiki/Stop_Enabling_Sex_Traffickers_Act

You're going too far ahead and wasting your time analyzing it...I'm not an Attorney btw....SESTA/FOSTA was, is and always be a bugos law...The opposition has not started yet..DOJ and State AG's, Other Law Enforcements, ACLU, etc are already commenting that it is a daunting task , it will take massive amount, personnels, time and taxpayers money to enforce it...to early to tell. it'll take time or maybe it will be frozen in court and be ignored till the next elections.....

It is NOT just about trafficking.  The law explicitly says that.  Criminal penalties and civil liability are spelled out for anything that "facilitates" or "promotes" prostitution of another person.  Nothing limits it to trafficking or coercion.  

Nothing in SESTA/FOSTA prevents a lady from advertising for herself and herself only.  Of course pandering and soliciting prostitution is and has been illegal in most states for a very long time, so that is and always has been the violation/risk for advertising.  

Could they be liable?

You can create a website and set up a server on your kitchen table and test it on your local area network (house) ... but you still need a way to connect to the internet. You need an ISP. Rather, a willing ISP.  
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How does the law discriminate between web hosting services (BP, CV, ... TER) and ISPs (Verizon, ATT, Xfinity, ...)?

"How does the law discriminate between web hosting services (BP, CV, ... TER) and ISPs (Verizon, ATT, Xfinity, ...)?"
If the language doesn't explicitly do so -- they don't.  They will go after web hosting services that don't censor client web pages.

One will need to set up the server at a Web Hosting company and get a domain registered. They will need to manage the server also. Many Web Hosting will allow it and it is no all that expensive.

I wouldn't think that paying a contractor to build a website for you would make the contractor liable. Technically all of the work (in this case, writing code) a contractor does belongs to the provider in this case, so the contractor couldn't be "trafficking" anyone because he's working for them.

Hold on, I understood the Trumpster had to sign the bill by 3/31 or it would be a pocket veto.  Did he actually sign it?  Can't find anything in the news about it at all.

Grrr, tomorrow? Fuck fuck fuck, tell him it’s too late his failure to sign in 10 days was an automatic veto and let congress come back to get the 2/3 votes from both houses.

Damn.  I was really hoping the monger would let it slide into oblivion.

Pocket veto can only occur if the congress is in recess.  Otherwise failure to sign is the same as signing.  Must explicitly veto if congress is in session.

But there is no mention that this has been presented to the President.  Thus, I don't think a pocket veto is applicable.