I'm only answering these where I have a strong opinion after just a glance at the board! Last time I was right, let's see about this one.

a feels like it must be correct on principle. It's one of those "both sides would love to have a stone here" points. If White plays it, the left side could be become big, there's more strength for reductions around K7 to reach out to, and Black's bottom stones could start to be weak (e.g., imagine White K4). If Black plays it, it's practically sente, all of Black's stones now feel strong, and suddenly a move like E9 feels scary.

b is also a good-for-both-sides point but doesn't feel like it has nearly the same urgency.

I don't feel any rush to play c; it's not like Black is going to play another move around here that will make the invasion more difficult in the future. Maybe a stronger player would play this as a probe that would influence how they would continue on the outside, but that sort of strategy is above my level.

a, but not for corner territory. It's for thickness and reverse sente.