You did just fine in posting this thread. At worse, if it was too similar, the posts would be moved to an existing thread. Thank you for conducting a search - that is more then some do before posting.
With the caveat that you acknowledge at the end of your post understood to be in place, I will attempt to answer this from my perspective.
Warning: I have a gaming background, which I’ve found makes my perspective different then some, sometimes in subtle ways and sometimes in not so subtle ways.
Now that all the caveats out of the way, I think the definition of “relationship” needs to be stated. Without knowing this, how can one design a game mechanic to represent a “relationship”.
The definition I use in my project is: A connection between two or more people.
Normally the stat_charts show the connection between the MC and an NPC but in theory it can also be used to display the connection between two NPCs.
As a designer, I decided to hide the connection between NPCs from my audience by making relationship mechanics between NPCs hidden.
Never-the-less, just as I track the connection the MC has with NPC1 and NPC2, I track the connection NPC1 has with NPC2. I’ve chosen to display this stat by prose and dialogue instead of a graphic bar.
So, a value in the relationship mechanic is relative to how well two characters are connected. A 100% value on my scale means the two characters are connected 100% and have perfect understand of each other.
In theory this is possible but using fair math, I deny this state from existing in-game. The reason I deny this state from ever happening in my game is simple: I desire the possibility that the two characters may mis-understand each other at any time. This is a hard-cap I place on this mechanic.
I view a displayed stat of 0% in my game as having no connection whatsoever between two characters. I also deny this state from ever happening. In my game, once met, two character have a chance to connect so there is an immediate increase in that stat to above 0%. This is a hard minimum I place on this mechanic. Again, fairmath is used to ensure the numeric never reaches 0.
Using my definition for relationship, I plan on having a standard in every game I design.
In your number 2 paragraph, things like secrets, shared experiences and other events that cause a connection to occur or break.
These events can be defined anywhere on that relationship scale using my design and as such flexibility is gained by setting flags at different milestones instead of being reliant on reaching and keeping those milestones surpassed.
Because I utilize my structure differently then many, a prose description of the relationship really does not apply. I get around this by having different “romantic” flags trigger special connections - play darts with Ellen in the pub and she connects with you as a fellow pub-game player. What the MC will do with this connection will be up to them.
Upon meeting, two characters make some sort of connection and depending on the characters, this varies in my game from 10-35 as a base value.
When I am playing other CS games, how I utilize the relationships depends on how the author developer structured their mechanic. In those games that I dislike the mechanic, I will try my best to ignore the relationship stats as much as possible.
With that in mind, I am trying to provide ways to connect in my game for those that try to ignore my stat-structure. I call these “Nexus points” and I track achieving these as achievements of their own.
I use these as “charisma builders” and the more the MC gathers, the more they will succeed in influencing relationships regardless of the actual connectivity they achieve in the normal mechanic.
I can’t answer number 5 yet because I am still tuning my stats and adjusting them.
I’m sorry for the wall of text - mechanics are important to me.