Down rounds are bad for employee morale too since it puts previously issued options below water. It's probably worth it to re-issue equity, but that's messy and a lot of companies don't do it.
At a previous company all of the employees (there weren't many left) demanded options be repriced. They were. Unfortunately, they still were worthless when the company was "acquired" in a fire sale.
Yep. But when your startup is burning through cash and you're not going to make next month's payroll, you're pretty much force to accept whatever terms you're offered. (Assuming you're offered any.)