Which sentence is correct?
1. The committee members resented the president that he did not tell them about the meeting.
2. The committee members resented the president's not informing them of the meeting.
Or you could use resented the fact that the president....
Or "The committee members resented the president for not telling them about the meeting".
Or "The committee members resented the president for not having told them about the meeting".
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.
1. What about this one: " ... that the president had failed informing themselves that there was going to be a meeting. "
2. Would you please tell me why we used possessive here? ( .... the president's not informing them ..... .)
It's the same reason we say "I appreciate your coming on such short notice" instead of "I appreciate you coming on such short notice." It's the "coming" that is appreciated, a noun, so the pronoun is the possessive form. However, most people either are unaware of this "rule" or choose to ignore it. You'll hear the non-genitive used all the time.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.