If I have a pinched nerve in my lower back can that cause numbness and tingling in all 4 limbs and would it be worse in the morning?

Unusual. Lower back nerves generally do not relate to upper extremities. Arthritis frequently is worse in the morning. Sounds like a good neurological exam for numbness, weakness , neuropathies etc. Is in order.
No. A pinched nerve in the low back or lumbar spine would be expected to affect the low back, hip and legs but not the arms.
Not likely, be seen. An entrapped nerve in your lower back would not affect your arms, only your legs. And, most likely, only one leg. You should see your doctor to find out what is causing the symptoms.
Could be. If you are sleeping in a position that exacerbates or makes it ticked off. You should sleep with knees bent and a pillow between and beneath your knees.