Here's a few answers.
To calculate pipe diameter and length, you need some engineering help. Call Pond Dam Piping at 800.333.2711. Also call Agri-Drain at 800.232.4742. Both companies can help. I would also recommend calling your local NRCS office and ask for engineering help. You must know volumes of water expected to flow during major rainfall events. That's the benchmark for deciding pipe size and length.
Next, a 2-1 slope is too steep. It will slough. You need a better grade.
Not only is an emergency spillway a good idea, I consider it critical. Pipe will be primary spillway, but without an emergency spillway, water can breech your dam. Plan an earthen spillway. Make it wide, and you can easily drive across it. Study topography..it may make sense to build your spillway well away from your dam. I have seen many lakes where the spillway topped a different ridge, especially for maximized sites.
Permits vary from state to state...but I would certainly understand the consequences before I put myself in a position to ask forgiveness.
Lastly...build during the driest months.

Teach a man to grow fish...
He can teach to catch fish...