What are the consequences of a possible solution to Yang-Mills existence and mass gap problem? Are the consequences only physical or they will also have applications to other branches of science or life? If yes, what are they?
I don't think that there are any new physical consequences. We already see asymptotic freedom, color confinement, chiral symmetry breaking; we are able to calculate hadron masses, form factoprs etc. on the lattice with < 5% deviation theor. - exp.
What's missing is a rigorous mathematical definition (or at least a proof of existence) of quantized non-abelian gauge theories and a rigorous derivation of the results. Confinement is still purely understood, most calculations are done numerically, ...
That's why it's a mathematical millenium problem ;-)