PulseAudio was used by previous versions of Raspbian, but was never pre-installed. The current recommended approach uses BlueALSA, but that is not included in the Lite version, I believe. So install BlueALSA, and find a recent tutorial for using Bluetooth audio streaming on a Pi.
Note that you can use the one-way A2DP profile, if your headset supports it, but two-way (speaker and microphone) HSP/HFP is much more complicated (if possible).
There isn't much out there for using Bluetooth audio streaming from the command line. Basically, install BlueALSA, pair (once) and connect using bluetoothctl, and hopefully your headset will auto-connect subsequently.
Aplay doesn't do mp3 files. You could try mpg321 or something else. I think you'll need to set BlueALSA as the default ALSA device.
Omxplayer requires you to use the '-o alsa' option, but you'll need to set BlueALSA as the default device. There are instructions for that on the BlueALSA web page. Kodi I have no idea about, you might visit their web page.