English question - please help?

Yes. This is totally grammatically correct, BUT it's all about appropriacy: It is very old fashioned Great Britain English, wouldn't be used except by people in the south of England who are over 45.

Perfectly correct, though a little formal.

'opening' is a gerund (a verbal noun), so needs 'my' in front of it.

Do you mind my opening the window?

Did you object to his eating the cheese?

I was unaware of your being an evangelical.

......

'Do you mind me opening the window?' is more likely what an English speaker would say. But it is very slangy, and you should avoid using such a phrase in an examination or a job application.

It absolutely is 100% correct against formal English grammatical rules.

In your sentence, the word "opening" is a noun - to be exact, it's a gerund (a verbal noun that looks exactly like the present participle), but it's very definitely a noun. Therefore, you need "my" before it, just as you would with any other noun (my coat, my car etc.)

Now, most English people will tell you that your sentence is wrong and that it should read:-

"Do you mind me opening the window?"

...because that how we'd all say it in conversation, but against formal English grammatical rules, they'd be wrong.

your grammer is perfect .but the way of speaking should be different . It should be like" would you mind if i asked you to open my window "

No it is:

"Do you mind me opening the window?"

NOPE it should read : Do you mind if I open the window? at least i think so btw i'm not a scholar:)