I have a prescription for hydrocodone. If I take Benadryl (diphenhydramine) along with it, will it decrease my chances of nausea?

No. Benadryl typically only helps with allergy like symptoms. Nausea is best treated with medicines like Phenergan (promethazine) or zofran. You may need to speak with your doctor to discuss these options. Often times changing your pain medicine to another one will resolve your nausea, again speak with your doctor.
No . It won't help if you have history of narcotic induced nausea and vomiting. Why are you using hydrocodone? What about trying non-narcotic medicine like tylenol (acetaminophen) or aleve. Any chronic pain syndrome? Don't use hydrocodone if not recommended by your physician with close follow up by him.
Not usually. Benadryl (diphenhydramine) helps with rash and itch. It doesn't really do much for nausea. Many Codeine derived medications (hydrocodone for one) cause nausea. Remember that hydrocodone is a narcotic and is addicting.
Yes. Taking your hydrocodone with Benadryl (diphenhydramine) will decrease the likelyhood of developing nausea, itching or a rash. Also having the medication with some food will help.
Maybe. If hydrocodone makes you nauseous then it would make sense to try something to combat that nausea. Sometimes specific anti nausea medicines like Phenergan (promethazine) or ondansetron / zofran can help. Bendadryl might help, but it will also probably make you extra sleepy.