1. What was Henk Angenent's record?

- He finished the race in 6 hours and 49 minutes.

2. What was Henk Angenent's record?
- His record was 6 hours and 49 minutes.
(Are both answers right?)

3. In 1963, how many percent of the skaters finished the race?
- Only one percent of the skaters finished the race.

(Is the question grammatical? Can we use other questions suitable for the answer?)

1 and 2 are both correct, yes.

For 3, here are two ways the question can be phrased:

In 1963, what percentage of the skaters finished the race?
or
In 1963, how many skaters finished the race?

The answer to both questions can be what you have written.