What is the ruling on leading congregational prayers in the mosque with a private corner, given the presence of blood and brownish discharge after a hemorrhoidectomy, and with the mosque being closed at many times?

The blood and discharges you mentioned, if they exit involuntarily, are excused. Your imamate (leading prayer) for someone who is ritually pure is valid, though disliked. This is the view of some scholars, like the Malikis, who consider the imamate of someone with incontinence or sores leading a ritually pure person to be disliked. The preponderant opinion is that the imamate of an excused person due to incontinence or similar conditions is valid for others.