EdifierR1010BT - 4" Bluetooth Wireless Creative Reference Multimedia Monitors - Studio Monitor Speaker (Pair) 24 Watts RMS - Black

Q: Can you connect a microphone (XLR) cable?

I don't think you can. These are consumers monitors, you don't need an audio interface to run them, therefore no XLR plugs.

Q: would these sound better than a soundbar for hook-up to tv?

any real speaker sounds better than a soundbar

Q: This has bluetooth 4.0, means delay transmission or cause lipsync?

Yeah, all Bluetooth has some kind of delay. If your just listening to music it should be fine but if your watching a video the audio will be slightly out of sync. You could always use the include auxiliary cable or dual RCA cable.

Q: Can they be use for my karaoke setup?

Besides Bluetooth you can connect these speakers wired using your basic red/white RCA connectors. If your karaoke machine outputs via RCA or Bluetooth, I would think the answer is yes.