First off, the correct preposition is "from." There seem to be few rules that determine which prepositions are correct, or, if there are rules, they are riddled with exceptions. The closest I can come to a justification is that the context implies a conversation, with comments coming from multiple "directions," where "directions" is a buried metaphor meaning different individuals. We commonly use "from" and "to" with directions.
Second, the plural "comments" seems far more natural than "comment" though both are grammatical. The reason is that what is usually contemplated is that more than one comment is expected and permitted. That is what distinguishes the example of "any comments" from "any doctor," where it is not contemplated that someone is going to sample the views of multiple doctors. In other words, what determines whether to use the singular or plural is not grammar, but rather intended meaning.
Finally, both sentences strike me as somewhat awkward, but this may be a purely personal reaction. I very much doubt that the speaker will appreciate any comment whatsoever. For example, the comment "You are a blithering idiot" will seldom be appreciated by the person soliciting comments.
Here is what is probably intended
I would appreciate your comments if you have any that are worthwhile and polite
which would usually get shortened to
I'd appreciate your comments
with the conditional implied by the use of the contraction of "would."