I'm Archmagister of House Telvanni, with a fully completed Stronghold and all. Just wandering around a bit now, and I had myself made member of House Hlaalu as well. So, I started doing some quests, got promoted and my next quest for Crurio would be to go to Odnirain (whatever) and help the survivers there.

Of course, at that point the game crashed, so, I haven't saved this yet, but... I've already done the same quest for House Telvanni, but then from the other point of view. And it made me think of quests to come (like go and kill the owner of Tell Uvirith). What's the deal here? Can I complete those quests and become Hlaalu Grandmaster? Or should I just remain content with a mediocre rank?

You can do all the quests except those relating to the stronghold (it is already built). If you talk to Crassius about killing the Redoran guy (Branden Indarys IIRC) he'll give you 1000 gold. You won't be asked to kill yourself. Do all quests for Nileno Dorvayn in Balmora; Crassius Curio and Edryni Arethi in the Hlaalu Compound (this also means working with Odral Helvi in Caldera) and Ilmeni Dren in St Delyn. If you have already completed her twin lamps quest you can get a third using the console by adding to her dialogue box 'people cannot read'. Once you have done quests up to getting the councillor Dram Bero on your side speak to Duke Dren, complete his quest and he will make you Grand Master. You now have two strongholds.

Cool! Thanks a lot, Malchik!
Two strongholds, eh? That'll come in handy... Albeit more confusing, tho! I can't even retrace most of my stuff as it is! Oh well.. The burden of property...