I bought the additional wireless plug for microphones, also from Bose, which works perfectly. The microphone is a Shure Beta 58 A. With this variant you are free to use other microphones as well.

I can't answer that. I am satisfied with the microphone I bought at the same time. (SE58)

That doesn't really matter at all. I have Shure SLXD, but a BLX from Shure works as well.

There are several wireless microphone options for the Bose S1 Pro system. One option is to use the Bose S1 Pro+ Wireless Mic/Line Transmitter - XLR, which connects directly to a standard XLR microphone and provides a wireless connection to the S1 Pro+ system. Please note that this transmitter is specifically designed for the S1 Pro+ system and may not be compatible with the original S1 Pro.

Another option is to use a wireless microphone system such as the Innopow 80-Channel Dual UHF Wireless Microphone, which is recommended in online forums for use with the Bose S1 Pro. You will need two XLR cables to connect this system to the S1 Pro.

Alternatively, you may want to consider a wireless microphone system such as the Shure SM58 Wireless, which is known for its reliability and sound quality. Bundles are available that combine the Bose S1 Pro system with the Shure SM58 Wireless microphone.

If you already have a favourite wired microphone, you can turn it into a wireless microphone with a wireless XLR transmitter such as the Bose S1 Pro+ Wireless Mic/Line Transmitter - XLR. A video tutorial shows how easy it is to use any microphone wirelessly with the Bose S1 Pro+ system.

Please ensure that the wireless microphone system you choose is compatible with your Bose S1 Pro system and meets your specific requirements.