1. I do not understand why this cannot go to equilibrium?

Na2CO3(aq)+HCl(aq)->H2O(l)+CO2(g)+NaCl(aq)

Please explain.

2. Are K subscript c the same as K subscript eq?
Do they both stand for the equilibrium constant?

a has been answered by Bob Pursley below.

Keq is the equilibrium constant. If you make a distinction, Kc is the concentration equilibrium constant while Kp is the partial pressure equilibrium constant. If I see a problem where K is listed I always assume it is Kc but that assumption is not always valid.