Is it normal for my feet to turn purple when I sit?

No. Even though this may not be normal it is not necessarily anything to be gravely concerned about. The best way to evaluate this is to have a lower extremity venous ultrasound to make sure you do not have significant venous insufficiency (particularly in the deep venous system). We see bluish discoloration in people who have had clots in the deep veins and then subsequently develop reflux.
Nope. This is not a normal color. This is commonly seen in people with venous insufficiency. The condition is called "dependent rubor". You already mentioned it happens when you sit. Have someone lift up your foot when sitting and if the color returns to normal than likely that is what you have. While not "normal", this is not serious either.
Probably not. I agree with dr. Aalami. Although it isn't normal, it might not be an alarming situation. It is not unknown for people with varicose veins, and no blood clots, to have their feet turn painlessly, purple with they sit. It may mean nothing more than having varicose veins that would benefit from treatment. Of course it is worth checking it out because it could be something more serious.
No. This could also be due to an arterial issue. Your feet may turn purple because you are not getting enough blood flow into your feet when you sit. Either arterial or venous should be evaluated.
NO. It is not normal for any part of you to turn purple. You may have venous obstruction when you sit, which causes the blood to pool in your legs, hence the purple discoloration. If it goes away with elevation or getting up and moving around, you probably have a venous issue.