What is the gas inside a Capsicum pepper, and how does it get there?
To answer your question of what the gas is, how about the glowing splint test for oxygen! I guess it might work with a recently snuffed out match too. Cut a plug in the the pepper but leave it in place until you have the glowing match ready, then quickly open the plug and hold the match into the opening. It should relight if it is oxygen and you may hear a popping noise.

As for whether the surface tension is preventing the flow of air, you could try adding some detergent (washing up liquid or soap) to the water to break the tension and see what happens. 

However, I have found an article suggesting the environment is, compared to the standard atmospheric concentration anyway, low in O2 and high in CO2 in two different pepper cultivars.1 


  Samples withdrawn from the fruit locule over time show that CO2 ranges between 0.5% and 3% (5000–30,000μmol·mol–1) (Fig. 2, top) while O2 ranges between 18% and 20% (Fig. 2, center), compared to the composition of standard atmosphere (400μmol·mol–1CO2; 21% O2)  




1 Blasiak, J., Kuang, A., Farhangi, C.S., and Musgrave, M.E. Roles of Intra-fruit Oxygen and Carbon Dioxide in Controlling Pepper (Capsicum annuum L.) Seed Development and Storage Reserve Deposition. J. AMER. SOC. HORT. SCI. (2006) 131(1):164–173.