Absolutely. As long as you qualify for each of them individually. Three states currently will offset your unemployment benefits by your Social Security (not the other way around) and they are...
I am 66 years of age and got laid off the same month that I started Social Security. Yes you can draw both. I live in California and have not had any problems.
Yes, you can if you want, but it's not necessary as you can receive both at the same time without either interfering with the other (unless you are in one of the states that offset unemployment by SS...