Can you descend with FLCH without selecting a lower level on your ALT select window? (Sorry, not familiar with Boeing acronyms)
Yes you can ... disconnecting the A/P and disregarding all the visual and aural caution!
Would you use FLCH for any approaches? BIG NO
If so, what is the minimum selected altitude? MDA?
NO FLCH for approach. But theoretically with the A/P engaged and pressing FLCH the Auto-throttle mode goes in THR reference and the FMA shows THR FLCH SPD with the speed window open and maintaining the current speed you have at the moment you pressed the FLCH switch.
And selecting the MDA in FLCH doesn't really make sense.
and finally, if and when, reaching the MDA, doesn't the Auto Throttle "awake"
If you use FCLH (which is not good for approaches) and you selected the MDA in the MCP the Auto-throttle system will maintain the selected speed in the MCP.