Questions about the ESE!Lupin theory

[acoteucla]

No: HPFGUIDX 73206

Ok, I've read some of the ESE!Lupin topics, and I'm very intrigued.  
There's gotta be a big betrayal somewhere in the last two books, and 
Lupin seems to fit the bill.  I have a couple questions before I jump 
on the bandwagon, though.

1 - Book 5: Why did Lupin prevent Harry from going through the veil?

It would have been very easy for him to pretend he hadn't noticed 
Harry running towards the veil.  One idea I had was that he wasn't 
saving Harry's life, but making sure Sirius was dead.  We have only 
Lupin's word that Sirius was dead the instant he fell through the 
veil.  Maybe if Harry had got in there immediately, he could have 
saved Sirius in some fashion.

2 - Book 3: Why did Lupin leave the map out for Snape to find?

There seems to be little reason for it.  Lupin can't possibly know 
that Snape was a spy for Dumbledore, else LV would have known, and LV 
would have killed Snape when he came back.  So why did he risk his 
plans in an attempt to kill Snape as well?  If Snape had gotten to 
the Shrieking Shack sooner, H/R/H would have been quite relieved to 
be saved from Lupin & Sirius.  Having Snape conscious would have been 
a huge risk to the success of Lupin's plan.