Numerical inverse Laplace transform

Questions
1

When using the Inverse Laplace Transform at a specific point, what is the default method for numerical integration if the function is monotonically decreasing with a singularity only at the origin?

3

You may try an experiment:

results = 
 InverseLaplaceTransform[1/(Sqrt[s + 1] + s), s, 5.3, 
    Method -> #] & /@ {Automatic, "Stehfest", "Piessens", "Talbot", 
   "Durbin", "Crump", "Papoulis", "Weeks"}
results - results[[1]]

It would seem that for this function the chosen method was Stehfest. From this

results - InverseLaplaceTransform[1/(Sqrt[s + 1] + s), s, 53/10]

it seems that the best method here is Talbot, but the difference from Stehfest is around MachinePrecision.