You can not say in general if the convergence with mesh refinement is from above or below - this can differ problem from problem, model from model.

You are right large elements are more brittle once a crack starts opening. For element sizes larger than the distance between localized cracks (typically, shells), please define crack spacing to prevent unrealistic brittleness.

I have a RC  pile cap with a coarse mesh. I was wondering which stress is considered for cracking criteria in FE mesh? is it the stress at element surface or the average for that element?

Does finer mesh give a higher load capacity and whilst the coarse mesh is conservative?

I guess the crack will propagate in the whole element (not partially) and with the coarse mesh it will be quicker. Please confirm if that is correct.

kind regards,
Siavash