To kick off this look at second chambers around the world past and present, let's look at the one other that has existed in the United Kingdom, the Senate of Northern Ireland which existed between 1921 and 1972.
As a brief disclaimer, I'm going to avoid wider issues such as gerrymandering, and the local government franchise. Whilst they were definitely part of the Stormont regime (although some of the gerrymandering originated at local level, though later reinforced by the Stormont government), they were not part of the Senate per se and can distort discussion of the structure.
Composition: 26 members (25 in practice from 1969). 24 elected by Single Transferable Vote by members of the Northern Ireland House of Commons with 12 elected at the start of each Parliament for two terms. The other two were the Lord Mayors of Belfast and Londonderry ex officio. In 1969 the Londonderry Corporation was suspended and no new elected body introduced before Stormont was prorogued. The Lord Mayor of Londonderry's seat was not filled.
Fairness of representation: One obvious distortion is that whilst the two county boroughs were directly represented, the six county council areas were not. (The gerrymandering of the Londonderry Corporation is widely known, but as the Mayor was elected by the councillors this point is perhaps beyond the scope of this analysis.) It's not clear at a glance if the Mayors were there to represent their cities, their councils, just the majorities on their councils or the people of the cities - four distinct (if sometimes confused) concepts. The 12 members elected at the start of each Parliament were elected by sitting members of the House of Commons. Abstenionist MPs thus did not have the opportunity to elect (abstentionist) Senators. Approximately 4 MPs were needed to elect 1 Senator, although with a sizable abstention this could reduce the quota. Micro parties in the Commons (and there were a number in the history of Stormont) would thus not be represented in the Senate unless they could band together. Consequently the 12 elected would be disproportionately representative of the larger parties in the Commons.
The precise political composition is not recorded as interest in the Senate was low but given the limited participation in the Commons by Nationalists, the fragmentation of opposition parties in the Commons and the addition of the Lord Mayors the chamber would have been even more Unionist dominated than the Commons.
The method for handling midterm vacancies isn't currently recorded on either webpage I'm linking to. Was there a convention that an opposition party with a vacancy could nominate a replacement unopposed?
Powers and conventions: I'm not too sure on these, although the Senate was regarded as "not designed to be a check on the legislature, but rather a place for reflection and revision of government bills - an additional means of finding parliamentary time" (Northern Ireland Elections: The Northern Ireland Senate, 1921-72) and in practice had virtually no political impact.
Conflict resolution: Again details are limited, especially as the Senate was never set up to be a check & balance on the Commons, whilst as both chambers were always controlled by the same party the potential for party conflict was minimal.
Protector against the tyranny of the majority vs bastion against democracy: This is rather more theoretical (especially given the limited information on powers and the lack of any reason to use them), but in terms of its composition the Senate could potentially have been a protector without being too much of a block to overwhelming changes in public opinion. As its composition reflected the outcome of two general elections it could resist a small change in opinion altering the balance of power in the Commons as at no point was even a bare majority of the Senate elected in one go. By contrast a landslide sweep of the Commons would bring with it many Senate seats and so securing a Senate majority would be possible for a new government with mass popular support. And as a government can call an election, what would there be to stop a new one calling an early election just to ensure it could get a majority in the upper house?
Because almost all the Senate was elected by the House of Commons, there was no opportunity for voters to "ticket split" and elect one party to a Commons majority and another to keep a check on them. And in any case it takes more than just composition but also actual powers for an upper house to take on the lower.
Anything else?: The Senate was created as an afterthought and it shows. Originally there would have been a single Senate for both Northern Ireland and Southern Ireland, but during the Government of Ireland Bill's passage through the Westminster Parliament this was amended to create separate Senates. (Northern Ireland Elections: The Senate of Southern Ireland, 1921) "Of course it developed into a sinecure for politicians who couldn't or wouldn't get into the lower house." (The Northern Ireland Senate. Op cit.) As early as 1926 there were calls for its abolition.
Anything worth copying?: Very little to be honest. The one point worth taking on board is the staggered elections. But having the upper house elected directly by the lower house is not particularly attractive as it primarily duplicates the lower house's composition, as well as creating opening for sinecures and placemen. And it is vulnerable to the ability of governments (or lower houses) to call a new election.
The inclusion of the two Mayors provided a link to local government, but it is a distortion of the role - Mayors are primarily chosen for civic municipal duties, not sitting in legislatures. (Executive Mayors, like the directly elected Mayors we now have in some areas, are as the name suggests executives, not legislators.) The idea of rotating mayoralties further makes it difficult to use them for a legislature as there is the risk a person will be chosen as Mayor for the sake of the legislature, not the municipality.