For supersonic acceleration (Mach 1 to about Mach 1.7), Concorde needed all four reheats (too much asymmetric thrust with three).
If one didn't light you could still do the accel. If two failed it was unlikely to work - what dictated whether it worked was not the number of reheats but getting to M1.7 by the 15' accel limit on reheat use - there was no problem with assymetrics. Actually somedays (e.g. cold OATs) the accel could outpace the fuel transfer, the technique then was to switch off one reheat to allow the fuel to catch up...
So if for whatever reason one of the reheats didn't light at the start of the take-off roll (which occasionally did happen), the take-off was abandoned, and the aircraft would return to the stand.
Again, not quite right. It was a matter of performance - if the TOW was a certain margin below PLTOW (using a graph in the performance manual) then you only needed 3 reheats (called a "GO" takeoff), otherwise you did need all four (called a "STOP" takeoff). This check was made at 100kts not 60kts - the NHP called "100kts" and if all was well the E/O called "power set" and off you went. Interestingly, a single reheat failure after 100kts did not constitute an engine failure and you carried on irrespective of TOW (rare: once lit they tended to stay lit - it was getting them lit that could be problematic....). Two reheats out constituted an engine failure and was treated in the conventional way...
Such a rejected take-off was a pretty straightforward affair, because the aircraft would usually not have reached more than about 50mph
See above - the reheat GO/NO-GO decision was made at 100kts.
Offered purely out of interest - hope it helps...