There are other choices out there that you might to consider, seeing as $350 is in your price range. The A&K M60 and the M249 are both viable options if you prefer those styles over the RPK.
To answer your questions:
1. A lot can be done, especially so as the gearbox is a V3. One can upgrade everything from the gears, to the piston, to the cylinder head, etc. A tight bore and a hop up bucking and nub will improve accuracy and range mostly. For a support gunner, these are both ideal, as is your ROF.
2. A 9.6v battery, at least, would be prefered over the 8.4v. The SRC gearbox can certainly handle a 9.6v and then some. Upgrading to a 9.6v will increase the trigger response as well as the ROF. If you wish to upgrade even furthur, such as a 10.8v or a Lipo battery, do some searching around here for information on upgrades needed to handle them. I do believe the SRC gearbox is plenty strong enough to handle a 11.1v lipo seeing as it has 7mm steel bearings and a steel gearset.
3. Whatever floats your boat! If you prefer the stock sights, use them. If you prefer a reflex sight, use it. If you prefer an eotech replica, use it. Get my point here?