Do I need to use any in the following sentence? Does any change the meaning of the following sentence?
If you have (any) questions on the subject, feel free to ask me.
As an English speaker would you leave any out?
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"Any" is a qualifier. It specifies what sort of questions are welcome.
If you have questions on the subject, feel free to ask me.
A student might feel that the question must be at least a certain quality before they should ask it.
If you have any questions on the subject, feel free to ask me.
The teacher is saying that all questions on the subject are welcome, no matter what the student might feel. It is friendlier and more likely to result in questions being asked than without "any".
Without "any" the student might assume only "good" questions, only "thoughtful" questions, only "short" questions, and so on. Including "any" is an attempt to counter the student's preconceptions about what sort of questions are welcome.
Taken very literally, "questions" means two or more, and "any questions" means one or more, even though it's grammatically plural. Most people would not be so pedantic in their interpretation of the sentence though.
As an English speaker, I would be much more likely to include "any" than to leave it out. It feels much more natural that way.