hmm, Well what I can say is price phister is a much disliked brand by many plumbers myself included as I find they are poor quality. That being said, there is no good reason for it to not work after like it did before. Try unscrewing the airator from the tip of the nozzle, like most threads it unscrews counter clockwise ( if you were looking at it from the sink up or straight at it ) these often have debris in them after a re model, and could be caused by wood shavings, drywall dust etc getting into it. unscrew and check the pressure, IF there is anything in the lines it should be able to be shot out with out the airator in place.
The angle stop is the shutoff valve, you find these on kitchen sinks, bathroom lavs and toilets also.
I am unsure about the "black line" I am not sure what this is ( pictures would help ) but make sure any lines you can see are free from kinks.
these "white pipes" you speak of, are they drainage pipes? or potablle water pipes?
there is enough watter pressure going down the drain to cause pooling, it could be a missed ring in a drainage slip joint, should be a simple fix.
Without seeing pictures I can only use imagination to configure and problem solve... I am sceptical of your plumbers ability, as I've yet to cross a line that was not easilly recognized and fixed immediatelly and BEFORE i left the job... and the last one I remember crossing occurred over 10 years ago when i was still a rookie.
I understand your frustrations as I respond to many calls of this nature, work done by boom time "plumbers" who are not as compitent as they would like to believe... again, that being said I dont want to crap all over your plumber... we all make mistakes, just make sure they fix them, and it should not cost you for their time to fix these problems, the lines should not have been crossed in the first place and if they wont eat the bill for their time to come out and un-cross them then I would seriously not use them ever again... that is shoddy.