Perhaps WoWHomeSolutions will come back in here and tell you what he considers the "normal" price range complete when they do garage floors.
I won't ask why you want to remove the new epoxy - unless it was 2-coated and should not have been, or second coat was done too soon so bottom coat never cured. If that is the case, prep cost will be higher than assumed below, because it will probably have to be chemically stripped because the gummy epoxy will gum up the machinery.
I would also ask but won't, why you want such an expensive floor for a basement - not usually done there. Commonly used in garages and warehouses because normal floor paints won't take the vehicle traffic, but for my money a normal good quality floor paint like Sears Weatherbeater Concrete and Deck paint works fine in normal basement use. Can get worn through in heavy use spots like where players are in ping-pong tables for instance, but ewasy to touch up and infinitely cheaper.
I am assuming you have 36" or wider door access to basement for the machine to pass through - how much narrower they could handle would depend on specific machine your contractor has. Be sure bidders are aware of access issues - door widths, stairs if any, etc.
One other factor - if you truly want the hardest floor coating, epoxy is not it - a polyurea or one of the other new-age coatings beats that hands down, but $7-10/SF for the coating (without grinding) as opposed to the $3-6 I gave below for epoxy.
Back to your questions, numbered as asked:
1) Can be ground if epoxy is hard, but with an intact epoxy coating I would think the contractor would prefer to use shotblasting, assuming the surface was already profiled correctly. If it needs profiling (smoothing and leveling) then grinding will be needed. Prices vary a GREAT deal - I have seen both large (chain grocery store sized) and small (residential garage or driveway) jobs go from $1/SF to over $4/SF. Or rent the machine (though does not collect dust anywhere as well) for about $100-200/day and do it yourself, with a 4" hand grinder with abrasive disc in the corners. Price depends a lot more on the contractor and what equipment he has in hand and if he needs work - I saw one garage job done with a commercial warehouse and airfield apron machine at a very decent price - was in and out in 15 minutes flat and a good portion of that was hand grinding the triangular-shaped corner areas the big machine could not get into. Contractor was just wanting to keep his crews paid so was taking on small jobs that week with whatever machine was available.
2) A new epoxy coat would not only probably not stick worth beans to a newish existing coat, but will likely soften and bubble it during curing, as all epoxy paints I have seen contain highly aggressive solvents. And I can't see a manufactuer or contractor offering a warranty on a coat-over job unless was their own product and application and very recently done.
3) I don't think there is a "typical" - depends on flatness and surface condition of concrete, working access, how much care they need to take to control dust from getting into the rest of the house, if a water heater or furnace is in the same area and needs to be protected from dust or even worse, isolated with a plastic sheet wall and temporary ventilation so it can stay running during the work (good reason to not do in winter), etc. $3-6/SF is what I commonly am told as a "ballpark" price for a normal 2-3 car garage which the client has totally cleaned out in advance so there is NOTHING in the way of the work except maybe a pedestal or platform that the water heater/furnace is sitting on. $3-4 range if cleaning and light surface prep like etching only required, $5-6 range if requires full diamond grinding first. That is for prep, epoxy coat with traction additive, and clear coating.
4) Should not have to if you can shut down any HVAC system, but you will have to specify that they are to provide high-volume ventilation to the outside during the active work and curing time. The strongest fume time is about 1 hour long - so you might plan a trip to the store or go out to dinner or something if you think it will bother you - otherwise just go out on the patio and drink pina coladas. If they use acid etching rather than grinding, then fumes could drive you out for a couple of hours early in the job.
5) Can physically be done in 1 day for normal sized area, but in a basement (as opposed to open ground-level garage) I would say assume probably 2-3 calendar days to do all work - not including moving stuff out and back in, which would be extra cost of course if they will even do it, plus 2-7 days curing time depending on brand and how much you are willing to risk scratches moving the furniture and such back in.