He's considered her "fiance"
Bride is to bridesmaids as groom is to groomsmen. Bride is to maid of honor as groom is to best man Here brides are to bridesmaids as grooms are to the best man.
the bride and the grooms name
It does not really matter whether it is the groom or bride's parents who call. In many cases the groom's parents call, but, etiquette does not dictate this.
The groom and the bride's fathers can both wear a tux. It would be okay for the groom's father to wear a nice suit because he would not be the one walking the bride down the isle.
The maid of honor is the opposite of best man in a wedding.
you write to Mr.and Mrs. John Smith (thats an example you would write the grooms name)
If they're of equal "rank" (social, military, professional etc.), then the groom's name goes first. If the bride outranks the groom, then her name goes first.
Orthodox Jewish grooms come for their brides after being apart from each other for a week. Other Jewish grooms come for their brides like everyone else.
Since it is the bride's mother who is sending out the invitations, which is customary then the return address should be to your parents or your mother.
They are not obliged to do this, but if the Mother of the Bride is in reduced circumstances , and the Groom's parents can afford it, it would be a lovely Bride's Gift from her new in-laws.
Most guests already know who the bride and grooms parents are and some weddings have a receiving line where guests congratulations the bride, groom and both sets of parents. If there is no receiving line then no, the bride and groom do not introduce their parents. The father's of either side may wish to make a toast to their new daughter-in-law or new son-in-law.
* Unless the bride so chooses to do so then no, the groom's mother does not get a gift. Both mothers should have corsages at the wedding.