"somebody doing" or "somebody's doing"

[xxwzs]

I am still confused with "transitive verb + somebody + doing" and "transitive verb + somebody's + doing". Four examples are listed below:
1. I can't imagine him running so fast.
2. I can't imagine her marrying that old man.
3. Do you mind me opening the window?
4. Do you mind my shutting the door?
I hope you can directly tell me which work/works well. I'd like you to point out what is/are the difference/differences between them and how I can use them correctly.
Still here waiting for you. Thanks!

 

[Rover_KE]

We're not expected to directly tell you anything.

We'll choose which questions to answer and do it in our own time.

 

[xxwzs]

We're not expected to directly tell you anything.

We'll choose which questions to answer and do it in our own time.

I am really really sorry for my bad wording. Pardon me please. In Chinese. expect is always translated as or something like "hope".
I don't know how to use the phrase in a right way.

 

[Matthew Wai]

In Chinese. expect is always translated as or something like "hope".

Ignore the Chinese translation “期望” and read the English definition: 'to demand that somebody will do something because it is their duty or responsibility'── quoted from
http://www.oxfordlearnersdictionaries.com/definition/english/expect?q=expect

All teachers here are volunteers, who have no official duty or responsibility to answer our questions.

I am not a teacher. I am a learner here like you.

 

[Rover_KE]

I am really really sorry for my bad wording. Pardon me please. In Chinese, expect is always translated as or something like "hope".
I don't know how to use the phrase in a right way.

Fair enough. Just say 'Please tell me which work well'.

1. I can't imagine him running so fast.
2. I can't imagine her marrying that old man.
3. Do you mind me opening the window?
4. Do you mind my shutting the door?

They all work well.

1. would sound unnatural with 'his'.
2. would be the same in either case, as the object pronoun her and the possessive adjective her are the same.*
3. would be OK with 'my', but would sound rather formal.
4. would sound less formal with 'me'.

*Click here for more information.

 

[xxwzs]

Ignore the Chinese translation “期望” and read the English definition: 'to demand that somebody will do something because it is their duty or responsibility'── quoted from
http://www.oxfordlearnersdictionaries.com/definition/english/expect?q=expect

All teachers here are volunteers, who have no official duty or responsibility to answer our questions.

I am not a teacher. I am a learner here like you.

Matthew Wai, thank you so much for helping me so many times. Your suggestions are significantly helpful to me. I think we can study English together and I can learn more from you in furture.