Learn Russian: Автор решил переписать черновик и доделать чистовик. - The author decided to rewrite the draft and finish the final draft.

The prefix пере- often adds the meaning of doing something over again, similar to the English prefix "re-". So, писать (to write) becomes переписать (to rewrite). Because it focuses on the completed result of rewriting, it is a perfective verb.

What does the prefix до- add to делать in the word доделать?

The prefix до- usually means taking an action all the way to the end or finishing it. While делать means "to do", доделать means "to finish doing" or "to complete". Like переписать, it is perfective because it focuses on reaching the final result.

The words черновик and чистовик look very similar. How are they formed?

They are a great example of Russian word-building. Черновик (rough draft) comes from the root чёрный (black), referring to a page messy with ink and corrections. Чистовик (final draft) comes from чистый (clean), meaning a neat, finished copy.

Why don't the endings of черновик and чистовик change here, since they are the direct objects of the verbs?

They actually are in the accusative case, which is required for direct objects. However, because they are masculine inanimate nouns (non-living things), their accusative form is identical to their nominative (dictionary) form. You only change the ending for animate (living) masculine nouns.