I gave the speaker to my grandson for his birthday and he is currently on holiday. Basically, you can use any microphone if the plug fits. I know this because I used to work in this business. For professionals, of course, there are better ones that are "wired" differently and would therefore not be compatible.
I don't have any specific information about a specific power cable to charge the Idance Party Groove Karaoke. However, the product is battery powered, which suggests that it could be supplied with a charging adapter or that a standard adapter could be used. It is advisable to check the product documentation or contact the manufacturer for precise information on the type of adapter required.
As soon as the box is paired with another device (mobile etc.) and the device is within range, the box cannot be paired with any other device. To do this, the box must first be unpaired. If the box is unable to establish a connection, it will become visible to your mobile.