Learn English – What’s the difference between ‘teacher of English’ and ‘English teacher’

"speak English" refers to an ability. "speak in English" refers to a language choice.

• Can/do you speak English?

  Meaning: Do you know English well enough to use it verbally?

• Can/could you speak in English?

  Meaning: I'd like to request that you speak English instead of some other language.

• Do you speak in English?

  That sentence doesn't make much sense, because "do" is asking about a habitual/continuous situation, whereas "in English" refers to a language choice rather than ability.

You did hard work.

or more naturally,

You worked hard.

says that the person put a lot of effort into the work. The former implies that the nature of the work is difficult, while the latter implies that the worker was very diligent in applying high effort. If you say

You worked a lot.

then you are saying that the person put a lot of time into their work, but are not necessarily implying that a lot of effort was required at any given time.

Use of the indefinite article "a" with "work" is archaic, I think. I see this usage in scriptural texts but not normally in conversation nor contemporary writing. Here "work" takes on the meaning of something that is coming about, rather than the effort taken by the workers.

Therefore, behold, I will proceed to do a marvellous work among this people, even a marvellous work and a wonder: for the wisdom of their wise men shall perish, and the understanding of their prudent men shall be hid.

That's archaic language from the King James Version of the Bible.