(a) never at. (b) it would be 'in the afternoon'. (c) If you use the plural, it changes the meaning from an implied 'this afternoon', to all/most afternoons. (d) You would usually say 'most afternoons'.

If you are talking about a specific time you can say 'at' eg. at 12:00 / at dawn/ at midday If it is a broader period you use 'in the' eg. in the morning, in the summer, in the afternoon.

I believe that many people do not use a preposition: "I am very happy to help you. I am available afternoonS." (The plural of "afternoon" is necessary.) If you wish to use a preposition, then you might say: "I am available in the afternoon/ afternoons." (The plural is optional with a preposition.)