Yes only seen it done the other way once in almost 2000 deals. Lawyers have strict rules about this, they can be disbarred if they fail to follow them

This happens all the time....because buyers and sellers are comfortable with attorneys they have had long standing business relationships with.

In NY, the seller's attorney holds the money in escrow. The attorney is not allowed to release the money to the seller until closing. If something should happen and you do not close, the attorney would have to return the money to your attorney, if it is something like not qualifying for your mortgage. If you just changed your mind, the seller would be able to keep the deposit. The seller's attorney still has to hold the money in escrow until everything is settled betweed your attorney and the seller's attorney.

Yes it is. Its completely normal