The reddish discolouration on the brick may just be dust from the bricks scrubbed off during the stripping process. It's very possible the company that did the work used a very aggressive rotary brush that had bristles impregnated with abrasives to do the stripping, and those abrasives would have abraded the surface of the brick. I would just use some acid on those reddish areas of mortar to remove the discoloured surface and see if it cleans up that red discolouration. (Then rinse with clean rinse water.) I would try using a phosphoric acid toilet bowl cleaner first to see if it's strong enough to dissolve the brick. The advantage of using toilet bowl cleaner is that it's gelled so that it sticks to the smooth sides of the bowl better, and that also prevents it from being "wicked in" to the mortar. The gel makes it too viscous to be wicked in, and so it remains on the surface of the mortar where it's needed, and therefore doesn't dissolve any more material than necessary.
Acidic toilet bowl cleaners come in both gelled phosphoric acid and gelled hydrochloric acid. The phosphoric acid based toilet bowl cleaners are milder than the hydrochloric acid based ones. I'd try using phosphoric acid first, and only move up to hydrochloric acid if the phosphoric acid doesn't work. The toilet bowl cleaner should say what the concentration of hydrochloric acid is, and it'll typically be anywhere from 7 to 30 percent. You should be able to buy both in various concentrations from the places listed under "Janitorial Equipment & Supplies" in your Yellow Pages phone directory.
I think it's kinda dumb that they used such a brush. If there were an acrylic finish on the brick, they probably didn't need to use such an aggressive brush. They probably used that brush because it was the only rotary brush they had.
I would re-seal the floors simply because they are porous and can be stained if you spill something on them. For example, Easter Egg Dye, Saniflush, wood stain or even beet juice would all leave a permanent stain in unsealed brick and mortar, whereas none of those liquids would likely penetrate through an acrylic sealer. The worst case scenario is that the sealer itself might be stained, but if push came to shove, you could always strip off the acrylic sealer and replace it.
I expect you could use any sort of stone or grout sealer on your brick and mortar floor. However, since this is a floor people are going to be walking on, you want to ensure that you get a sealer that dries to a HARD film that will stand up well to foot traffic. I would find out who the local Diversey sales rep in your area is, and find out what he'd recommend putting on a brick and mortar floor. Diversey is the new name for the commercial and industrial floor finishing division of the S. C. Johnson Wax Company.
Nowadays, no acrylic sealers yellow with age anymore. Years ago, that was common, but thanks to the wonders of modern chemistry, that problem has pretty well been solved and you shouldn't have any trouble getting a non-yellowing acrylic sealer nowadays.
Much of the information that applies to your floor also applies to other masonary floors like slate flooring. There is a thread in the Flooring forum entitled "Slate Floor Maintenance" that I posted in, and much of what's in that post would also apply to your floor. You might want to read my post in that thread over.
I would use an acid to remove the reddish discolouration before sealing the floor. And, yes, you can seal this floor yourself.