Facing is cutting the ends of the tube to make them smooth and parallel to each other. Reaming is (I think) cutting out the bore of the tube to ensure it’s the right size. Generally you shouldn’t need them doing (imho) but I did need the headtube of my last frame faced (my LBS face and ream as part of the same process I believe) to get the cups to sit properly.
I’d go along with the others, if you’re struggling go along to the LBS and get it done properly rather than whacking it with a mallet, there is the danger of wrecking both the headset and frame!
I was charged £20 for facing and reaming together. I’ve no experience of zero stack headset or headtubes though.