The damage shown is unlikely to cause a structural problem. Once you reassemble, torquing the arm on very tightly, you should feel no wiggle of either crank arm relative to the other one. If, after some riding, you find some wiggle, torque the arms on more (within spec). As long as there is no wiggle, the damage will not cause any problems. There is not enough alloy missing to weaken, just to potentially maladjust the tapered fit.
The noise you were hearing could have been any of a number of things: a loose crank arm (fairly unlikely if you hadn't removed it recently), a pedal, or the bottom bracket. Check the pedals first -- they should turn freely and without grinding or noise. Service or replace the pedals if not. If the pedals are ok, then test the bottom bracket. Since you have the crank arms off, make sure that the spindle turns freely and without grinding or noise. Also check that it does not have any play by trying to wiggle it up and down or front and back. If there is noise, binding, or play, service the bottom bracket.
In the future, use a crank puller with a smaller push surface. Alternatively, you can loosen the screw in the crank spindle a few turns without removing it and have the puller push on that. If that screw head prevents the puller from threading into the crank arm far enough, you can put a screw with a smaller head into the spindle and push on that. That will extend the spindle enough to prevent the pushing surface from going into the tapered opening in the crank arm.