Lets say I get a RX200. Can I charge the batteries while in the device or do I need a separate charger. Also which batteries would you recommend.
The short answer is yes, the rx200 will happily charge your batteries.
The long answer that the last two posts (one recommending Google, and the other lecturing the first on a technicality) didn't give you is yes, but a dedicated, external charger is recommended, even in many cases by the manufacturers of these devices that can charge internally.
The biggest problem, from my understanding, is uneven charging and discharging of the batteries over time. Followed by that, the worry that you might wear out the USB port that in many mods is now also used for firmware updates.
There are others, I'm sure, but that's what comes to mind.
That all said, I cheaped out a month ago when I got my kbox 120 and have been charging the batteries in it nightly via usb without issue. I occasionally rotate the batteries in their bays in case it charges/discharges unevenly. It's been fine. This is with a pair of LG hg2 cells bought together and only used together.
I'm pretty sure that the manufacturers recommendation of an external charger is, in general, a CYA move in case anything goes wrong when someone charges in the device. They can just say "we said you should use an external charger". We're dealing with lithium ion batteries, which can get nasty when things go wrong. They just don't want to be held responsible if it does. At the same time, established brands usually won't put out utterly nonfunctional product. It hurts the brand if batteries start boring up in their mods.
Finally, I should say that the risk-aversion part of my brain is compromised, as I ride, and grew up on, motorcycles. Sitting on top of a series of explosions that propels two wheels balancing down the road is my baseline of safety. Take everything I say (and anyone else for that matter) with a grain of salt. Don't cry to me if you do what I do, charge in your mod and something goes wrong.
If batteries get hot, though, abort, disconnect, stop.
EDIT/PS:
gopher byrd's info and links above on batteries are important if you are unfamiliar with lithium ion cells. Read and understand that before you take any of my advise.