It is called bricklaying and tuckpointing, and if you can find similar brick and do it correctly it should be fine. If you don't have an idea where to start... hire a bricklayer or someone in masonry/tuckpointing.

Are you sure what you removed was plaster and not mortar? In either case, it's not really clear what you want to do. If you want to have the brick exposed and visible then you have a sizable job in front of you replacing the mortar by tuck pointing the joints- after removing any crumbling mortar bit by bit - where it has failed or been removed. This is quite a bit more than a "cosmetic repair". The mortar is what holds the chimney together. If you want to coat the entire surface with something there would seem to have been little point in removing what was already there. You would still need to do some fairly major repair work on the chimney before proceeding as well. Honestly and without wishing to be unduly alarming, the photos show a chimney in dire need of evaluation by a mason or other professional. By chipping off whatever was present, you may have seriously weakened the chimney. The mortar is in very poor condition and I would guess that there are many loose bricks. The expanding foam product shown in the bottom photo provides no strength and is unsuitable for repairing masonry. A coating of some sort and some paint is not going to fix this.

You need to attach wooden furring strips to the brick, and screw the sheet rock to the furring strips. You can glue the furring strips on the brick with a construction adhesive that bonds on contact (Loctite Power Grab). The key is to make the thickness of the furring strip + 1/2" sheet rock come out even with the rest of the wall. You'll need 4 furring strips - one on each end, and one on each corner:

I have no experience with the Proform system which appears to be pretty new. I'd check on Hearth.com for further information and opinions. I did have a Supaflu liner installed more than 20 years ago which has performed extremely well without any problems at all. Others, however, have apparently experienced serious deterioration which may be due to improper mixing of the liner material. A cursory look at the Proform website shows that the liner is installed then inflated and cured with steam. This is different from Supaflu which pumps a semiliquid slurry around an inflated former. The material strengthens the interior of the chimney because it makes its way into any voids in the mortar and becomes firmly attached to the brick from bottom to top. I don't think this happens with Proform. I also don't think it's really possible to pour a true footer from within the chimney. Footers should be wider than the chimney and support its weight from below. Stuccoing (parging?) the interior would also be very difficult. Using this method on the exterior would be possible, but would not be, in my opinion, as secure as repointing the brick. Proform may be an excellent lining system, but doesn't seem to really do much for rebuilding and restoring your chimney. Rebuilding brick by brick, then using a stainless liner, which are fine, seems a better option to me.