Why is the takeoff minimum acceleration height 400 ft but the go-around is 800 feet?
400 ft third segment is historical and based on early ICAO documents. I am not aware of any standardised requirement for a miss at 800 ft, although that is quite common throughout the Industry. Generally, you will be initiating the miss at or above whatever the relevant height is for the particular approach. Main thing to keep in mind is that the required configurations are different for OEI/AEO.
Also, an obstacle must be cleared by 35 feet on the net flight path. Surely if I were repairing the roof on my local church and a B777 with one engine on fire came over my head 35 feet above me this would be somewhat alarming?
Alarming all around. Keeping in mind that the gross gradient will be somewhat better than the net, and the height delta increases the further downstream we go, you should expect an increasing clearance as the takeoff continues. If the failure is well after V1 (ie better than the AFM story) then you should be well and truly higher than necessary in most situations. The crew should see the gross gradient (or a little bit better) while we run the clearance sums based on a degraded net gradient presumption.