The answer to your question on charging is yes, but do you need to, is another question.
If charging from the surface then you would need the proper charger used for LiPo Batteries in the ROV and because the tether will have a significant voltage drop before it gets to the ROV then the voltage at the surface will have to be something much higher. This brings into play other safety issues and there have been many discussions on both in this form on that very topic.
The OpenROV team have been testing different batteries and have found some that out perform the LiPo batteries but I have not seen or tested them myself. Because I am not using the OpenROV housing and I have lots of Boyancy, my ROV has the batteries mounted inside the ROV. Using this last summer I was able to get Hours of Dive time on one charge, and that was using bigger motors than what is used on the OpenROV today. This winter I have switched to the same motors as those used by OpenROV and I expect to get even longer battery life.
If you decide to try the charging battery from the surface scenario please share with us your results but play safe when working with higher voltages. You can also search this site for discussions by others who have been playing with this.
As for the batteries that I use: http://www.hobbyking.com/hobbyking/store/__9184__Turnigy_5000mAh_3S_20C_Lipo_Pack.html