Early exercise / 83(b) has another benefit that most people aren't aware of -- if the exit is at least 5 years out, you can exclude 100% of your gain from federal cap gains tax under IRS Section 1202.
No, it's at the discretion of the company. I asked for an 83(b) option at a 10 person startup I worked at and the CEO made it happen. The startup still went under so it didn't matter in the end, but management definitely did what they could for the employees.