Generally, no. Unemployment usually is only available for employees who have been laid off. Not fired for cause. Some states may allow for it, but the vast majority do not.
Not necessarily true. Firing for cause can be interpreted many ways. In my state about the only way a terminated employee can not get unemployment on the cause issue is if the cause involved moral terpitude, , ie on the job theft, assault, etc.
Now if you voluntarily resign, that is a different story.