I have #3 pick in my draft tomorrow, it's a considerably weak draft so I'm considering not signing the pick and getting the pick next year. Lets say I sign an IFA right now that leaves me with ~3m left in prospect budget. Do I still receive my compensation next year for not signing my first rounder this year? If yes, what pick will it be?

You only get compensation if you offer him his requested amount and he declines. 

Thank you sir

The #3 pick that will sign will take 3.82m.    If you draft a "May sign if the deal is right", I believe his initial request will be for more.    I think drafting the "Undecided..." with his mommy as his agent is the safe route to get a contract decline.   But you need that 3.82m.   And he may take it.

Kudos buddy. If it works, what pick do I get next year?

4.

Unless #1 or #2 also get comp for unsigned picks.

I don't think anyone other than "Will sign for slot money" players ask for only slot money... everyone else asks for at least a little over slot.  "May sign..." is usually slightly more, "Undecided..." is quite a bit more and "Probably won't sign..." is at least $6,000,000 and usually $8,000,000 or more. 
I have had at least one "Probably won't sign..." take my initial offer (when I certainly didn't want him to), but "May sign..." & "Undecided..." seem to accept the initial offer pretty often, and almost always not reject you outright (as in, they come back asking for more money... which you DO NOT need to offer to get a compensation pick) 

Ive never seen "probably won't sign" ever come back with an offer.  They just dont sign.  How rare is it for them to actually sign?