Should I just lie in bed and avoid exercise if I am having extra back pain?

No. Lying in bed can worsen back pain because muscles will atrophy (weaken) if not used. Strong back muscles (through a regular strengthening program) is one of the keys to alleviating back pain.
No. Laying in bed for too long can actually make back pain worse. You should avoid exercise initially (in the first day), but then start to incorporate stretches and exercises gradually.
No. There are many different reasons why you might be having extra back pain. You will have to have an idea why you are having back pain before deciding on what to do. If due to strain/overwork/heavy lifting, then you might need a short period of rest (1-2 days) with some pain pills, and gradually resume your usual activity.
No. We used to think that a period of convalescence was required for acute back pain, but we now know that this can lead to deconditioning of the muscles of the back which could make the situation worse in the long run. For acute back pain, just continue your usual activities but avoid anything physically strenuous or laborious.
No. For most back pain, lying in bed can actually worsen the problem. Lying in bed causes muscles to stiffen up (think about being stiff when you wake up in the am), & can also lead to muscle deconditioning & atrophy. Try to remain "gently active"--move around, but don't lift things, strain. Warm showers, massage, later on some gentle stretching, & then later core strengthening. Neuro symptoms need doc eval.
Yes. The best recommendation i can give you is to have a complete evaluation, x-rays, laboratory tests, etc to determine the etiology of your pain. Pain in the back could be related to several conditions - fracture vertebrae, herniated disc, spinal stenosis, lumbago, abdominal aortic aneurisym, etc. Do not take for granted that your back pain is only related to strain. You must have a diagnosis and tx.