I'm no expert, but I might be able to help some with this.

1) Not sure what the highest rank would be - it kind of depends on what you think makes a rank "high" - but Master I think would be most appropriate, personally. I believe that being part of the politics and having a certain amount of power within the Telvanni are two different, albeit related, things. It's kind of like two separate ranking systems - council and mouth are roles within the Telvanni society, whereas Master and wizard and such indicate power, experience, and a certain amount of pull. Therefore it might be more of a requirement to have a certain amount of power to obtain a political position, but not technically necessary. A master, for example, could hold a very high rank politically, but does not need to be terribly involved. They would still be considered a master, and would therefore have a lot of respect.
2) Archmagister is basically just top dog of magisters, as far as I'm aware.
3)Mouth would probably be considered a role and special rank all in its own. I don't think it's necessary to go up in the ranks to first hold this position, but rather it's a rank meant for a more specific job.
4) From what I can tell, the council behaves kind of like a small governing body, setting the laws of the Telvanni and making decisions as they do. Many Telvanni, because they value more power and ability than anything else, don't give a damn about the politics, but others like to use their magical prowess to gain political influence. It's like, as I said before, there's a ranking system of power levels among the Telvanni, and that first and foremost determines respect that a Telvanni should get. After that, there's a separate political system, in which having a certain power level helps an individual manipulate things. The two exist separately, but definitely influence each other. Again, I'm no expert, so it's probably best to take this with a grain of salt, but from what I know this is how the House behaves.

If you're looking to make ranks for a guild, I'd probably go and set up a few ranks by power level - whatever you determine to be the lowest level to the highest - and then fit in a few political ranks right next to the "power" rank that people with that political position normally have. The political ranks could have the same permissions, but then have additional roles within the guild, such as determining rules and events and such.

Anyway, hope this offers some insight, and if anyone has something to correct me on, please let me know. I'm not Loremaster Lawrence Schick after all.

Actually to support a discussion. We already have developed the ranking system for our Rp, which we hope to be most lore friendly. It is based on the TES3 and developed a bit, according to what we have in ESO:

House Administration
Archmagister
First among equals of the wizard lords of the Great House Telvanni, who demonstrated exceptional magical power. Formally, he is the head of the Council.

Councilor
Politically active Magisters who form the Council of the Great House Telvanni. They are represented by their respective Mouths.

Mouth
Young and politically active Telvanni mages, commonly of the rank Spellwright or Wizard. They represent interesets of their masters in the Council; negotiating and making decisions on their behalf.

General Ranks
Magister
The peak of Telvanni nobility, their authority is unquestionable. Magisters form the general impression of Great House Telvanni - they traditionally isolated themselves, pursuing wisdom and mastery in solitude.

Master Wizard
The high tier of Telvanni nobility - Master Wizards are the mages who demostrated exceptional wisdom gathered after centuries of research. They prefer to stay away from politics, devoting themselves to science.

Wizard
The majority of Telvanni nobility. Mages who earned their position by hard work and display exemplary knowledge. Like other wizards, they mostly devote themselves to research, but also take part in politics to some degree.

Spellwright
The lower level of Telvanni nobility. Young but powerful mages who have demonstrated considerable magical talent. They may still be apprentices, but spellwrights can conduct their own, independent research.

Lawman
Not noble members of the House, who have made their way to this level with hard work, or who have it by right of blood. They proved their value to the House. Lawmen are not actively involved in House politics. Mostly, they are apprentices and less often independent researchers or battle mages. Telvanni who do not engage in research, cannot rise above this rank.

Oathman
Telvanni commoners, who have proven their loyalty to the House. Commonly, they are apprentices, experienced guards and traders. They may own slaves.

Retainer
Young members of the House, who demonstrated their usefulness. They carry out various assignments for higher-ranking house members and can become assistants of Wizards. For further advancement, they must find the support of a Telvanni with a rank higher than Oathman, under whose guidance they will serve. Retainers are not eligible to own slaves.

Hireling
New members of the House. They are allowed to use public laboratories and libraries. Nevertheless, the study of magical arts is not mandatory for them. Mages, as a rule, do not stay in this rank for a long time, while soldiers are often content with this position.

But as i said, it is still assuption, even if they are made on strong Lore basis. That is why opinion of Loremaster is crucial.

Mighty admis, i summon you to help proceeding questions in first post to Loremaster. please
@ZOS_JessicaFolsom @ZOS_GinaBruno @ZOS_Lawrence_Schick

Keep in mind there is a significant passage of time from the era of ESO and Morrowind, so that could explain any changes in rank structure...plus you know .....dragonbreak

Hireling
Retainer
Oathman
Lawman
Mouth
Spellwright
Wizard
Master
Magister
Archmagister

Those are the ranks according to TES3. Note that upon reaching the Magister rank you signal that you want to threaten the Archmagister so it wouldn't make sense to have one. (Not sure if this is something touched on in ESO Morrowind as i haven't finished it yet). Since there's only ine Archmagister it wouldn't make sense to have a player character playing him or her as he or she probably exists in Morrowind anyway.

To progress to the rank of Master and above you also need to have your own stronghold (though you can start building it from Mouth and above). I imagine the lack of area also prohibits too many Masters from existing as you can only carve up the area to so many pieces
Also reaching Master rank will automatically make you qualify for Magister and hence a threat to the Archmagister. So Wizard seems like a good place to stop for player characters

Also it seems that all the Masters are also part of the Council although i guess some could choose to isolate themselves and not take part in the political race