I am taking oral nsaids for a lumbar herniated disc conservative treatment. How long should I take them? Is there a standard duration?

Long term . You to use them till the pain stop, then you could see if you cut them in half and see if the will under control. You have to be sure you do not develop any complications in the process.
It depends. You definitely take them for at least 2-3 weeks, always with food. You mention conservative treatment, that should include physical therapy and back exercises . If you can't stop nsaid, discuss with your physician the use of acid-blocking agents - either h2 receptor antagonists such as Famotidine or proton pump inhibitors (omeprazole and the like). You also should monitor bp, blood and urine tests.