If you have a gun engraved does it have to be reblued?
No re-Blue is called for, if one wants the incised/engraved lines to be silver color. And, sometimes things are done this way.
If you have a nickel finish, does it have to be redone after engraving?
See above, but, probably, usually, the Nickel plating would be removed prior to the engraving process, and, then, finial finish would be decided and applied.
Historically, Guns were engraved 'In the White' and then Blued or Nickeled or Gilded or combinations of these or as may be.
Recent times, various creative Liberties are sometimes indulged...where a Blued Gun is engraved right through the Blueing and left just as that.