Sounds both in head set and speakers

I think it won't be possible to get rid of the feedback and quality will be poor when recording this way. Try software like Audacity and set the audio source to record directly from the sound card. The input device should be set to "Windows WASAPI" for Windows and output set to a loopback device.
How to Record the Sound Coming From Your PC Even Without Stereo Mix

could be, make sure the sound on the laptop is working watch a video and play music anything to noise on the laptop.also click the speaker icon by the clock check volume settings no muted. make sure headset in earphone jack and no volume control on headset

You need to check the audio output device is set to bluetooth on the laptop, on which you will also have to pair the headset, but since I have no idea what the laptop is or what the operating system is on the laptop, I can't help, however this may be of help:

Most computers will only pair this earpiece as a headset for voice calls. You need to make sure the headset is paired with your device as both a phone headset and media headset. Check your settings on your computer or smartphone to make sure it is paired properly to play media sound.

I would suggest you to use a headset (without mic) and play the karaoke for them so that they can listen the music through the headphone while they sing. Connect the mic on the mic plug on your computer and record the songs they are singing with rhythm of the karaoke using an audio editor like Audacity or Adobe Audition and similar softwares. Suppose if you play the karaoke on your speaker, then the music will be heard from the mic and it'll be mixed up with the songs he/she is singing. For best result, Record the sound/songs and save it as different file and mixdown the karaoke file with it later. Otherwise, you'll not be able to get good songs. Please let me know if you need further help.
Good luck.
Thanks for using FixYa.

u need check u r sound setting click on sound icon on u r taskbar and then click on properties and playback or recording click on microphone and try to scroll lolz try dear

Yea, you can, you need to co to control panel and under sounds set the 360 head set control which will be your microsoft wireless control to default....but the sound is crapy..it seems that the manufacturers never designed this device for that kinda sound, only those who are talking to you with another mic...so i suggest sticking with your speakers or a good set of ear phones

Dear Biswaranjan.
the volume control on media player before that there is one button for speaker click on it and sound will come from media player. I think you have muted on media player.

i think ur not using nokia approved genuine headset accessory . even though some head sets have nokia logo they r not original made by nokia . they cause low sound quality while hearing music and diaphram bets can be heard during playing high bass songs . try with another genuine headset

thanks for the update.