Shrink the paper or pay for extra page charges?

You already have the answer from your advisor. He is the one who knows the circumstances and can make the call if he want to.

You can ask, but be careful how you do it. Remember, if he wanted to do it, he would have done it already instead of asking you to cut the paper.

Yes, if its close enough, and he feels that grant has been supporting his activities...

Generally yes (depends on whether the grant is tied to any specific spending though, e.g. staff costs, equipment, etc.) - but if the advisor suggests to cut down the paper, it is probably best to follow that suggestion. An alternative would be to provide the longer version of the paper as an official technical report by the university, which should not clash with publication restrictions of the journal. I have seen a number of publications that have a technical report with the same title. (This is in computer science.)

See above - but this also depends on the relationship with the advisor. If they're generally friendly, suggesting it sounds reasonable ("would this be an option...?").

Yes.