The Lords of Waterdeep are a democratic council
Drawing upon some older sources that do have information on this. Here is some from FR1 Waterdeep and the North (1st edition AD&D):
Waterdeep is presently governed by sixteen Lords of Waterdeep, who are seen by the general populace only when sitting in the Lord's Court, identities concealed by identical masks and robes. It is rare indeed for more than seven Lords to sit in Court on a given occasion. This democratic council has a largely secret membership.
Democratic council pointing towards each member having an equal vote. City of Splendors (AD&D, 2nd Edition, "CoS") expands on this (p. 27):
Ahghairon seated himself, then, and proclaimed himself the first Lord of Waterdeep, saying that henceforth wisdom and not armed might would rule in the city. He would gather some few - in secret - to rule as Lords with him, masked and disguised when they appeared to the people, but equal to him in authority and free of coercion by any, himself included. These
Lords could serve as long as they wished, and were to be drawn from all walks of life in the city.
Which means, that the Open Lord has no more voting rights than any of the Masked Lords. They may have additional executive powers in from additional offices such as (page 15)
Warden of Waterdeep (= commander of the City Guard), Overmaster of the Guilds, and Commander of the Watch
But these are not giving them more decision making power in the Lord's council. This is also confirmed on page 67:
By keeping the identities of the Lords of the city confidential, Ahghairon made them of equal power with himself and guaranteed that they would be "free of coercion by any, and drawn from all walks of life within our fair city."
In political practice
In how far this is holding up in practice however may be a question. According to the history cited on page 27, after Ahghairon's death, the guilds disposed of most of the Masked Lords, and ruled the city for a time, until they in turn were overthrown again by the last remaining two Masked Lords. Much depends on the favor of the popluation and the nobility in such situations:
The surviving nobles came, reluctantly and with bodyguards,
expecting such a summons to be a trap. Baeron spoke to them and the crowd of curious townsfolk that had also come, saying, "this must not happen again." If Waterdeep was to be safe once more, he told them, all must support what he and his fellow Lord now planned, as they had supported Ahghairon in the past. The two would choose others to be Lords as before, he said, and they would rule in secret, as before - save for himself. He removed his mask,
and said, "I am Baeron. I would be Lord as Ahghairon was before. I would be safe in this my city again." And the folk of Waterdeep there agreed.
Also, during Aghairon's time, it seems that practical power played an important role, as he took to removing a errant council member by force, "free of coercion" seemed to carry only so far:
Of the august membership, only one Lord - now nearly forgotten, but once known as Kerrigan the Arcanist - ever abused his power, and paid the price for his treason. Kerrigan, through various subterfuges and hired agents, killed three of his fellow Lords before Ahghairon discovered his treason. A spell battle erupted between the two, which crossed the city and ended in Southern Ward with the death of Kerrigan.
Your specific questions
- Are decisions made by the council decided by a simple majority?
Yes. The whole setup of the council which states are all members are equal in authority, means that no member. including the Open Lord, can have more voting powers than any other, and in such cases a majority vote is the most natural way to decide. So for a democratic council, in the absence of other information, we can pretty safely assume it.
2.a Are there any term limits, or do Lords serve until death / retirement? Can they choose to retire from the position at any time?
Lords can serve as long as they wish, page 13, FR1:
These Lords could serve as long as they wished, and were to be drawn from all walks of life in the city.
They thus can retire or step down. The Lord Caldorn for example did so (CoS, p. 69)
For two years, Caladorn stepped down from the Lords
to wander the Sword Coast and recover from a broken heart
2.b Can the Open Lord remove them from office at will or must this be done via the Council (and again, is it a simple majority?)
Considering that the Open Lord is only equal in authority to any other Lord, they cannot and it must be a council decision. Otherwise, the other Lords would not be "free of coercion" by the Open Lord - the Open Lord could just remove them from office, against their will.
No Information is provided on quotas. Majority rule would appear the simplest, although often in company statutes, changes to the composition of the voting body require a higher majority like two thirds -- unless someone can find a citation, this will be up to you.
- How does this "impeachment" happen? Can it be effected by the Masked Lords of Waterdeep, and if so -- again -- is this done by simple majority or some other mechanism?
This must be a majority vote by the council, as no Lord has more authority than another. On voting quota, no information is given, see above.
- Can Masked Lords of Waterdeep nominate or elect other Masked Lords, or is this entirely down to the Open Lord?
Any Lord can sponsor someone to be a Lord, and they need to be elected by vote from the council. There is an example of the halfling Nindil Jalbuck being elected to the council in CoS, Book IV, p. 6.
Nindil was given the mantle of a Lord of Waterdeep. His nomination was sponsored by Danilo Thann, a new Lord himself in 1364, and supported by Mirt, Durnan, Kitten, and Brian.
Shieldmeet Council
The Forgotten Realms Campaign Set has this to say on Shieldmeet:
Shieldmeet: Once every four years, another day is added to the year in the manner of February 29 in the Gregorian calendar. This day is part of no month and follows Midsummer Night. It is known as Shieldmeet. It is a day of open council between nobles and people; a day for the making and renewing of pacts, oaths, and agreements; tournaments, tests and trials for those wishing to advance in battle fame or clerical standing; for entertainment of all types, particularly theatrical; and for dueling
Shielmeet council is the session of the Lords that is held on Shieldmeet. As that day has a tradition for renewing agreements, this council -- considering the patchy history of the city when it comes to the Lord's rule -- serves to reaffirm that the way the city is goverend remains unchanged, and the Lords remain in power.
There was an incident (CoS p. 31) in DR 1364, when
A green dragon and an apparently mad bard disrupt the Shieldmeet ceremonies at the Field of Triumph, nearly upsetting the Lords' Rule
So in the eyes of the population, the orderly conduct of Shieldmeet appears important as a sign of the Lords' ability to govern.