FADH2 and NADH can supply the redox power and have an important role in the respiration chain. Is there any relations between them or whether they can replace each other in some reactions?
There are both cofactors for oxidoreductase enzymes, but they have different redox potentials and different electrochemistry. Also, FAD is usually a bound cofactor and NAD a diffusion cofactor, so your electrode mediation, etc. is typically different for FAD-dependent oxidoreductases and NAD-dependent oxidoreductases.
FAD derived from riboflavin, vitamin B2, where NAD may be synthesized from tryptophan. However, FAD can accept two hydrogens while NAD can accept one hydrogen, electron transfer by FADh2 produces less ATP than by NADH.
Are you working with proteins or are you simply looking for an electron donor? As Dr. Minteer said, they are quite distinct electrochemically. In terms of the biochemistry of these cofactors: for metabolic reasons, proteins are incredibly specific to their cofactor (even if they are similar in size and function) and usually cannot be substituted. I spent two years exploring cofactor specificity in an oxidoreductase and was never able to get it to accept an alternate cofactor (NADPH to NADH). But it's not impossible...
FAD or FADH2 is a prosthetic group (i.e. a cofactor that is covalently bound with enzymes such as succinate dehydrogenase), but NAD+ or NADH is a co-enzyme (i.e. a cofactor that is necessary for activity of certain oxido-reductases/ dehydrogenases such as malate dehydroenase). These two redox agents have different redox potentials and cannot replace each other. Energy of donatable electrons associated NADH is significantly higher than those associated with FADH2. Accordingly, H+ gradient built by the electrons donated by NADH is more than those donated by FADH2 [therefore, number of ATP generated by NADH is more (generally assumed to be ~3) than that of FADH2 (i.e. assumed to be ~2). With regard to electron donations capacity, both FADH2 as well as NADH can donate two electrons at a time.