Yes it is safe, all microwaves work on the same principle, and use the same range of radio frequencies to heat food. All microwaves used to be flatbeds, most commercial microwaves are still flatbeds, so you have nothing to worry about.
Yes, you can use a honing steel with a damascus-style carbon steel knife blade. Depending on what you have, you may need to get a harder honing steel, because the carbon steel of the knife is harder than a stainless blade. I have a honing steel from Shun that works quite well.
Do NOT use that "Anysharp" sharpener or any sharpener like it. Such sharpeners ...
Damascus steel was carbon steel with non-uniform carbon content (to give ripple pattern). It would be sharpened the same as any other steel knife. I don't know how a knife made today with the name "Damascus" is made. For my ordinary stainless ( typically 420 = 13% Cr ) I usually just use the wet stone and don't bother with the steel.