Can nitric acid be used to create an acidic medium for redox reactions?
Yes, you can.

However, nitric acid is an oxidizer, so it can interfere in some cases. If a strong reducer (like magnesium) is involved, nitric acid may act as an oxidizer even in diluted solutions. Obiously, it acts as an oxidizer in concentrated solutions, producing rather nasty nitrogen oxides, and if used without prior knowledge, it may produce unstable explosives. 

For this reason, one generally use hydrochloric acid or sulfuric acid. Mind you, in case oxidation is not a problem, nitric acid may be used with no problems. Another reason to use sulfuric acid is that it is dirt cheap. It is the cheapest alternative. 

Still, in concentrated solutions sulfuric acid does show oxidating properties, so in some cases sulfuric acid is not suitable either. Unfortunately, there is no common and reasonable alternative in the case, except significanlty weaker phosphoric acid.