While we can say it's not necessary, it's not redundant either (be careful of this mistake). In English, sometimes a certain amount of "verbal padding" is used to get the right tone and sentiment across. In this example, I understand the "should" as meaning "if it were to happen that..." Very polite and indirect indeed! You can also rephrase the first part as "Should you change your mind..." You'll see this form in polite business correspondence.

It's not *necessary*, but it makes the sentence sound a bit more polite. The 'do' in 'do let me know' is the same - you can leave it out but including it adds a bit of politeness, like you are inviting the reader to contact you. I would see (and use myself) this kind of usage quite often in formal or semi-formal business emails.

Yes, the sentence would still be correct without the 'should' - but the meaning would be different. We often use modals and the subjunctive form to distance ourselves from a situation, and to suggest that a situation would unlikely. 'If you change your mind' implies that there is maybe a 50/50 change that you will change your mind. However, 'If you should change your mind' implies that this situation is possible but improbable. So, for example, when you buy or book something with a company, they might send you a letter saying 'If you should change your mind, you may cancel within 14 days ....' . The company don't want you to cancel, and they are implying that their product or service is so good that you wouldn't want to change your mind. But - just in case - in the unlikely event that you should change your mind, you may cancel within 14 days. It's all about likelihood.