Hi! Welcome to RCG.
No, I've got two of these Celectra chargers and they do not overcharge batteries. At least the LED on them turns off after charging my 1S 3.7V lipos after around 25-30 minutes. I take them off the charger then. Don't know where you read that review but it's not supposed to do that...
Here's one review:
I think this is a good charger but it would be good to consider looking around for a cheaper price.
I use this charger:
but it takes a bit to get it set up and you have to buy a separate adapter to charge EFlite batteries in parallel. Charging in parallel has to be done carefully as well and some people in the RC community do not think its safe (for good reason...)
As for batteries, you could consider these:
They're cheap ($1.69 each) but should deliver enough juice for your MSRX. They probably won't last as long as the more expensive ones but then again you should probably only fly the MSRX for 4-5 minutes at a time because the motors will die quickly if used continuously for too long.
Another battery you could consider is this one:
but these are thicker than the other ones I posted and will split the battery holder on your skids if you crash as they're a very tight fit.