Barbara,
It looks from the pictures as if it is Altro flooring (the non-slip stuff).
Should feel rough when you run your hand over the surface!
If that is the case, I would suggest that you try Prochems Ultrapac Renovate, a standard speed rotary and plenty of Black/Brown pads. Make up a strong solution of chemical and mop hand hot water on generously, leave for 10 mins, then start scrubbing, stubborn marks will need you to get down on your knees and give it some welly, using perhaps neat chemical, clean the floor a bit at a time, do not try to clean the whole floor in one hit.
As suggested by Access, use a "Doodle Bug" (Edge Scrubber

) for the edges, and the most stubborn marks.
Once you have scrubbed an area, use a decent wet and dry to remove the slurry, go back and check the area, removing any remaining marks by hand.
Move to another area, and repeat.
If it is Altro, using a stripper will do you no good, as there should be no seal or polish to remove, yes I know others say that you can put a water based polish on altro, but in my opinion you risk damaging the anti slip properties of the flooring, and you would never get the manufacturer to state in writing that you can put polish on the floor when there is a danger of the floor getting wet.
Regarding pricing for the floor, this again depends on how confident your are of getting the job done in one pass so to speak, and how close you are to water, and the waste area. I can see no reason why you shouldnt complete the job in a day, providing the floor is in one main area with a 2 man team.
Labour cost would be £320
Chemicals approx £60
Pads £40
As for the remainder, I would need more details, such as surfaces, sizes, walls etc.
Do not under price this one, it will be hard work if all the floor is in that sort of state, and you will only really know, if you got it right when finished, you gain experience on this one, then use that knowledge, to get closer the next time round, sorry couldnt be more help!
Regards,
Rob