1. Fogg must be back in London by 21st December.

2. Fogg must be back in London by December 21st.

(Are both correct? Is #1 a british expression?)

3. Do it, and I pay you 20,000 pounds.
4. Do it, and I will pay you 20,000 pounds.

(Which one is correct? Are both grammatical? Do they have difference in meaning?)

1 and 2 are correct, and yes, 1 is British.

3 is incorrect. 4 is correct.