Are these affirmations correct ?
I have a diploma in speaking english. I have a diploma/degree in nursing.
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I have a diploma/degree in Nursing.
Yes, that is correct.
I have a diploma/degree in speaking english.
While that doesn't appear grammatically incorrect, necessarily, there aren't diplomas in "speaking English" which I have ever heard of. The degree would be in "English Literature", or perhaps "English", or "English Philology". Almost all diplomas and degrees have a certain official form about them. "Speaking english" is just a casual phrase, instead of an official title.