I had surgery for an abdominal hernia a month ago. The area below the scar has remained numb and sore. The internal scar is hard. Is this normal?

Normal. After such an operation, it is not unusual to feel a firm (hard) ridge under the scar. This represents healing of the tissue beneath the skin and can present as you describe. This can take several months to resolve. Check with your surgeon as he would have the specific details of your surgery.
Yes it can be. I do not know what type of abdominal hernia surgery that you had. If it was a transverse incision, then it is common to temporarily have some mild swelling above the scar, firmness along the scar itself, and numbness below the scar. This can last for several weeks after surgery and usually slowly resolves as internal healing continues, and the skin sensory nerves grow back into the region.
Probably. It can take 6 or 8 months for innervation to return to normal after a surgery - and sometimes there is a permanent decrease in senstation as a result of surgery. Depending on the materials used to repair the hernia, the area my have a different texture for days, weeks, months, or permanently.