Let me just explain all I know on this.
A vaginectomy is not a procedure done on it's own for trans males as far as i know, it is done in conjunction with metoidioplasty or phalloplasty.
They cannot lengthen the urethra without a vaginectomy, and you cannot have a vaginectomy without some sort of urethral lengthening. No, pee does not come out of the vagina, but with a vaginectomy, they usually use the labia to form a scrotum, and if not they kinda sew it up to make it look like a male perineum (medical term for the gooch, if you don't know). It doesn't need to be lengthened to the tip of the penis but it does have to be moved out a tiny bit so its in the same place, but is past where it is sutured shut or behind the scrotum.
A hysterectomy must be done first. If there is fluids (blood, etc) that needs to be released from the uterus, it has no way out if you remove the vagina.
Lastly, not all "vaginectomies" are not actually full vaginectomy. A full vaginectomy is far more difficult and risky and is usually only done in cases of cancer. I'm not entirely sure what they usually do for trans men, but it is a lesser procedure.