Yes. It could be. An md can help correctly diagnosing your pain.
Can be. Buttock pain is frequent with most back pain syndromes. This can occur with pinched nerves in the back, inflammation or degeneration of various structures in the back. Very common symptom.
Yes Its Possible. This pain in the distribution as you suggested is the result of an irritated nerve or facet joints or other injury typically in the lumbar spine (low back) which are caused by herniated disks, spinal stenosis or degenerative disc disease, etc requiring further evaluation by a spine specialist.
Possiby. There are many things that can cause "butt pain". Sciatica is one of them. See your doc for further testing.
Can be. Sciatica is usually caused by the sciatic nerve being compressed in the buttock area by the piriformis muscle, so yes, this can also cause butt pain. Other causes include myofascial trigger points in the gluteus maximus/medius/minimus muscles. Lumbar facet joints and the sacroiliac joint also frequently cause butt pain.