Strength of Mix For Gate Pier Footings

[Eugbug]

Apologies in advance, this is a long winded post!

So I'm building a concrete gate pier, 18" square by 53" tall. I'm butting it against an existing solid concrete wall (8" x 3' approx). I'm going for more of a spread footing because ground is boulder clay from what I can make out, not stuff that has to be broken with a pick. I'm going to making the foundation twice the width of the pier, 36" in one direction (so that's a 9" projection each side of the 18" pier). Also I can tie the pier to the wall for support, and my gates (about 5 1/2' wide by 4 1/2' tall) are unlikely to be over 80kg. I know this because I made a tall side gate for the side of my house previously using 2" x 1" box frame, 1 inch flat for scrolls and gun barrel and that had an area not much less and it was 40kg.So I don't need a heavy footing to counterbalance the gate.

Some questions:

I have no problem with the foundation on 3 sides, but to extend the footing beyond the base of the pier towards the adjacent wall (which will be butted against the pier) I would have to undercut the wall and remove a section of it's footing. Do I need to do this, or could I rely on the wall as a support for the pier to stop it leaning towards it? It's a 30 foot solid wall. If I don't extend the pier's footing, it will be sitting on the edge.

I planned to make the foundation 12" deep, should I make it even deeper? E.g. 18"?

What strength mix should I use for the footing? I have seen C25 mentioned on forums?

I don't understand the progression in the strength of mixes

C20 is 1:2:4 cement, sand, stone
C25 is 1:1:2
C30 is 1:2:3

C25 has a higher proportion of cement than C20 and is stronger than it, but a higher proportion of cement than C30 and is weaker? I know the stone/sand ratio is also of significance, but does it follow that less cement and a stronger result can be produced by simply making a C30 mix?
Are these ratios correct?

[Eugbug]

Didn't get any replies, so went with a 1:3:1, cement, stone, sand mix.
Made the footings twice the with of the pier I'm going to cast and 18" deep.