The results are not going to be the “same”. The longer the delay between neighbor list rebuilds, the larger the chance that you are missing the contribution of interacting pairs of atoms within the cutoff because they have moved inside the cutoff range since the last neighbor list rebuild. Since you are using a rather large cutoff the differences (in potential energy) due to the missed contributions will be very small. A setting for “delay 20” is at the limit of what is an acceptable choice for your kind of system. The total energy is not a good parameter since the differences due to the missed interactions is small relative to the total energy.
Regardless of whether the neighborlist rebuilds are done sufficiently frequent or not, if you build neighbor lists on different timesteps, you will change the order in which forces are summed up, which will lead to small numerical differences on the forces (due to limitations of floating point math) and thus to exponentially diverging trajectories. They will still be statistically equivalent.
Dangerous builds are a consequence of the neighbor list skin and a check that LAMMPS is doing when a neigh_modify check yes setting is used. This is based on a heuristic: if any atom has moved more than half the neighbor list skin distance since the last neighbor list build, the current update is considered “dangerous”, i.e. there is a risk, that some interacting pair has been missed in the force computation of the time step(s) before the one where the neighbor list build happens. This heuristic of a half the skin distance is very conservative, so you can have dangerous builds and still correct neighbor lists. However, if you have no dangerous builds, it is certain that all neighbor lists were correct.
Yes, that is because the time consuming rebuild of the neighbor list is deferred until the neighbor list check heuristic is reached, and the check for it is fast. Please have a look at the timing summary and the number of neighbor list rebuilds. Your second case enforces a neighbor list rebuild in every step and that is not needed at all. About every 10 steps should be a safe choice and every 20 is probably still acceptable, even if you may miss a very distant pair occasionally since your cutoff is so large.