What did Snape know about the Map and Messrs M, W, P & P?

As I have said several times before, The Prisoner of Azkaban is probably my favourite of the Harry Potter books and films. So I approach reading this third novel with a great deal of anticipation and, most often, I sit down to the watch the film when I am coming to the end of the book.

I just love the way the film presents the time-turner elements of the story at the end.

My most recent reading, however, has raised some confusion in my mind, confusion with regard to what is actually going on in the scene in which Snape and Lupin square off over the discovery of the Marauders Map in Harry's possession.

What does Snape know about that map? And about "Messrs Moony, Wormtail, Padfoot and Prongs", its creators?

Certainly, he appears to know a great deal: when he says to Lupin, "You don't think it more likely that he got it directly from the manufacturers", he seems to be indicating that he knows that Lupin and his friends created the map and that Lupin had, in fact, given it to Harry.

So why, then, does Snape allow Lupin to lie to him so blatantly in claiming that the map "looks like a Zonko product to me"?

And why doesn't Snape keep the map and take it to Dumbledore as evidence to support his theory that Lupin is helping his old friend Sirius Black?

We know that Snape is fully aware that Lupin is a werewolf (suggesting the nickname "Moony"); why would Snape not then be able to start to unravel what the other nicknames imply and then figure out how Sirius was able to get past the Dementors and enter the school?

I'm not trying to be critical; I am simply confused. Am I reading this wrong? Is Snape not fully aware of who the manufacturers of the Marauders Map were? Help me figure this out.

A couple of other points on The Prisoner of Azkaban:

On at least two occasions in this book (when Neville breaks a tea cup in Divination and when Hagrid drops a milk jug in his hut), we see magical characters scurry to clean up the mess. Why didn't they deal with the mess with magic?

In the film, when Lupin has his Defence Against the Dark Arts class first face the Boggart, we actually see the Boggart transform into a Dementor on Harry's turn. Lupin doesn't intervene until we, and everyone else, actually see the Dementor. Why, then, does Lupin later suggest that he intervened because he thought it would turn into Lord Voldemort?

In the book, Lupin intervenes before the Boggart transforms, which makes his explanation plausible. But, in the film the Dementor actually appears before Lupin steps in...

Two things to think about, I guess. And please help me to understand what Snape knew and did not know about the Marauders Map and the various nicknames for Lupin and his friends.