The COOLPIX L830 does not recharge batteries internally within the camera. If rechargeable batteries are to be used with the COOLPIX L830, they would have to be charged externally. The batteries that are compatible with the COOLPIX L830 are lithium and alkaline AA batteries. These AA batteries can be rechargeable type and can be inserted into the camera.

Blur is most frequently caused by movement of the subject or camera. There are several different ways to approach preventing motion blur. Using the L830's built in flash will help, but may not be appropriate for all shooting situations. Try switching to the L830's Best Shot Selector which takes a series of photos and saves the sharpest one. Best Shot Selector can be found in the Continuous section of the Shooting Menu. Vibration Reduction (Photo VR) and Motion Detection can help reduce the effect of camera shake and subject movement. You can find these options in the Setup Menu. If these tips don't help, please contact Nikon Support for further assistance.

Yes, the COOLPIX L830 can shoot in Macro and Monochrome/Black&White modes.

This sounds like there could be a problem with your memory card. Please check the COOLPIX L830 Manual or contact Nikon Support for information on memory cards that are approved for use with the L830.