1. He works over time on the weekend.

Question

2. He works over time over the weekend.
3. He works over time during the weekend.
4. He works over time this weekend.
5. He works over time this coming weekend.
6. He worked over time last weekend.

(Are they all grammatical? Do you have some more expressions which can be used with 'weekend'?)

7. Shall we have a race?
8. Shall we run a race?
9. Shall we take a race?

(Are they all correct? What other expressions can be used with 'race'?)

Answer 1

In 1-6, I think you mean "overtime" not "over time" -- there's a difference. "Overtime" refers to working later than usual, often for extra money.

With that correction, 1-4 and 6 will be correct. 5 needs to have a future tense main verb in order to refer to the coming weekend.