A:AnswerYes, but you really shouldn't. Just like you shouldn't leave other products like phones and such plugged in all the time when they're already charged.
A:AnswerA nintendo branded nunchuk does not need batteries as it is powered from the wiimote. if you have an off brand nunchuk that is wireless that varies on brand.
A:AnswerI looked everywhere for rechargeable batteries only. I have a Nyko Rechargeable Battery Station where only one of the batteries cannot hold a charge. I purchased the energizer station just for batteries although I wish I could just order the batteries. Now I'm thinking of a rechargeable Quad Station. I can't believe I am still playing with my original Wii, now with my 5yr old grandson.
A:AnswerMy experience with this issue come in with a damaged wiimote. it would do a similar thing because the contacts wouldn't properly touch the battery pack contacts. If you have another wiimote try it in that and see if you get the same issue.