There is always a V1 and it is always less than, or equal to, VR. At come weights the calculated VR might be less than V1 but, in such cases, VR is increased to equal V1.

On most takeoffs an abort after V1 is possible for a brief period but there's no way to know when that period would end so the only aborts after V1 are when control is lost or the ability of the airplane to fly is seriously in doubt. An abort after VR is unlikely to end well.

Minor items which would trigger a low-speed abort (generally under 80 to 100 knots) are not enough to justify a high-speed abort (from ~100 knots until V1). Once in the high-speed portion of the takeoff, aborts will likely only be accomplished for serious problems such as engine failure, engine fire or loss of directional control. The decision is the Captain's.

The tires have thermal plugs which are designed to pop allowing the tires to deflate when the tire temperatures rises too high. This prevents overheated tires from exploding and causing more damage and possibly a fire. After a high-speed abort the possibility of brake/tire fire is the prime concern. There are brake cooling charts which specify a minimum amount of time that must elapse, without any tires blowing their thermal plugs, before another takeoff can be attempted.