Broken off screws can be extracted using a hand pin chuck, but it's time consuming. Make a hole then tap a modellers three faced file into the end and draw out by unscrewing with pliers...…………...
Where possible I try to fill holes with a sawdust/wood glue mix, which can then be re-drilled……..
I also use matches...and ash always needs a pilot hole...…….try drilling it and it's exceptionally hard.
