Do you mind opening the door?

Hi,

Welcome to the Forum.

Q1  Sentence A expresses the speaker's request to the listener.

A: Would you mind opening the door?

But does B also express the speaker's request?

B: Do you mind opening the door?

I think the speaker's request can be expressed by using "Would", so B doesn't express request. Am I right? In evryday and common English, both A and B mean the same thing. So, if I wanted to express the meaning you describe below, I'd say it differently to make my menaing unambiguous.  eg

Would you rather not open the door?

Would it bother you to open the door?

Is it a problem for you to open the door?   

I think in B the speaker, knowing the listener has ever opened the window, asks if the listener wants to avoid the act of opening the door.
Am I right?

Q2  Can you use "Would you mind --- ing?" to express the general act of request?

   That is; can you use such sentences as "Would you mind helping me when I am in need?

Hi,

A: Would you mind opening the door?

B: Do you mind opening the door?

You wrote: "In everyday and common English, both A and B mean the same thing." Of course you meant both are used for

I'd like to know why B can be used for expressing request. First let me explain. My idea is, ----- the speaker can ask whether the listener is unwilling to open the door or not only when the speaker requires such an action of the listener. So B should be expressing request.
Am I right? If I really thought there was a definite possibility that the person might object to opening the door, I'd probably say A. I'd also say A if I wanted to be very polite. However, opening the door in most cases is a small and trivial thing, so the more direct B is not unusual.

Are you often in a situation where you ask someone to open the door, and you find that the person is unwilling to do it?

Best wishes again, Clive