Does lack of blinking cause any problems?

Dry eyes. Blinking wets the front of the eye, which is dried by contact with air.
Lack of blinking. Lack of blinking can cause dry eye and eye irritation. I would try artificial tears frequently during the day, ointment at night, warm compresses 1-2 times a day, and omega-3 fatty acid supplements. If no improvement, see an eye doctor.
Yes. Lack of blinking can cause the tears to break down as the layers of the tears can separate between blinks. Usually we blink about every 5- 6 seconds or 10-12 times a minute. Any less than that and the tears cannot do their job of keeping the ocular surface smooth.