According to the OED Online’s advanced search function there are:

22,561 nouns from Latin
16,189 adjectives
4,106 verbs
442 adverbs
34 interjections
28 prepositions
3 pronouns
2 interjections

Some of these are double counted. A word that is both noun and adjective counts in both categories.

Do you mean ultimately from Latin, or directly from Latin?

Seems quite a low count.

I don’t know what the OED’s exact criteria are in determining this. It’s just the product of their search function.

As a point of comparison, the word Latin appears 57,994 times in the etymology section of words. That would include all references to the language, not just derivations from it. Since the combined counts from the other method are 43+K, I would imagine that those numbers include non-direct imports from Latin.

The absolute count is arbitrary in many ways. The relative counts, the ratios between the parts of speech, are probably pretty reasonable though.