Is it safe to have a nerve block administered?

Yes. I have done thousands without\ serious issues to my patients, except for bleeding from a punctured deep blood vessell. If properly done, great pain relief can be obtained.
Generally yes. Your anesthesiologist will cover the risks/benefits prior to doing. In many cases it may be safer than general anesthesia or opioids for pain, though there are risks. I personally am a big fan, though opinions vary.