Because importar works here with an indirect object: something matters to someone.
So:
Think of importar here as working like:
So the person affected is introduced with le, not lo.
Because Spanish often leaves subject pronouns out when they are clear from context.
Here, you already know it is usted because:
So usted is understood and does not need to be stated.
You could say ¿A usted le importa...? for emphasis, but normally that would sound unnecessary.
Because after si in this sentence, Spanish uses the indicative, not the subjunctive.
Here si means if / whether, and the speaker is asking about a real possible action:
So:
This is a very common learner question because English does not make this distinction in the same way.
Because cerrar is a stem-changing verb.
In the present tense, the e in the stem changes to ie in most forms:
So cierro means I close.
This is just a normal conjugation pattern, not something special caused by the sentence.
Because Disculpe is not part of the question itself. It is a separate polite opener.
Spanish punctuation marks only the part that is actually a question:
This is very normal in Spanish.
Yes, that is also possible and natural.
There is a small difference in structure:
Both can mean Do you mind if I close the window?
The version with que cierre uses the subjunctive after importa que, which is also a very standard Spanish pattern. Learners often meet both versions.
Yes, several alternatives are natural in Spain, depending on the level of politeness:
The original sentence is already perfectly natural and polite. It is a good option when speaking formally.