Protek batteries are crap. Look at Liperior (not the Endurance line), CNHL (G+ series), Zippy compact, Turnigy, or SMC.
Not sure about tires, I'm using stock tires. Maybe one of the other mini B people can answer that one.
Id go as far to say as long as its not dipping under 6V under load, I wouldnt worry about it. Putting smaller tires on it would help or as Nino said, a better quality battery might help but it will be hard to find one the right size for that car without modding the battery tray a bit.