I generally find it best to do these when you either literally have two (or however many are involved) writers characters in a relatively small or time dependent space. For instance, we're doing a crime caper RP. Our characters are in the elevator down to the garage getting ready to start this job.

The timespan is tightly defined, the involved characters are tightly defined, and if this goes on for pages because no one wants to not get a little more in it will look stupid.

Collaboration allows us all to monitor how long the post is going and cut out some extraneous dialogue. If my character says something dumb the other two characters can roll their eyes and say something like "we dont have time for jokes, we're almost there" and if I'm irritated with that we can massage the dialogue out until everyone is happy rather than go off on a tangent.

They're also handy when you're doing a lot or getting into deep lore for multiple characters or factions. This can be as simple as collaborating by saying "Hey, I've got a post for Danathar The Barbarian but it involves him talking about the Scythiaron Rebel Alliance you're writing...can you give it a once over and let me know if I have misconstrued something?"

It can be very useful.

Absolutely a thing. Generally used by the OP or Original Poster, the person who started the story off or is running the story.

These can be great to jump from one big event to how the characters or groups have adapted to the consequences of that big event. Everyone could always allude to what has happened between that event and the current time if they desire to.

Ex:
The Last of us, if I recall correctly, you don't follow Joel in real time from the introduction cutscene through to the final cutscene. Nor is that the case in the sequel. There's a time jump from the intro cutscene and that limited gameplay to the gameplay with Ellie that makes up the bulk of the first game. Likewise there's a time jump from the ending of the first game to the beginning of the bulk of the gameplay in the second game.

You could still write an entire story about what happened during those time jumps, but it serves the story they wanted to tell to just jump forward a bit.

Another Ex:
I once did this for a Fallout RP. A previous RP had ended when all our characters got tangled up in a big war with another faction. Everyone had stopped posting. I waited quite some time and then wrote what was originally intended to be a short Fan Fiction based around a time jump to the very end of that war. We had defeated the enemy, at great cost, and were just mopping up some their sinister work. Specifically we were freeing folks who had been enslaved by raiders. It ended up catching the interest of all the writers of that first RP because I mentioned characters that weren't explicitly but quite implicitly their characters. Ended up sparking off a whole new RP with a new cast of characters and several returning but changed ones.

Yes.

The more moving parts the more useful these things are.

In a 1x1 RP taking place in a single room involving two characters there is very little need for any of this. Your partner knows your characters name. Both your characters are in the same place at the same time. No Heading is needed as all of that was established in the opening post and re-established in each subsequent post. Colors aren't needed because there's only two characters talking and your partner can reasonably be expected to deduce what is his own characters dialogue and what is your characters dialogue.

As more and more characters, factions, locations, and dialogues become involved these things become more helpful or even borderline necessary.

If we're doing a United Nations RP, with 8 posters, wherein there is some great enemy, let's say Aliens, all our nations are trying to attack/defend from/reason with/sabotage it pretty quickly becomes very helpful to define these things at the start of every post. This is also where a time skip will eventually likely be necessary.

Ex:

United States of America
Washington D.C.
White House
Situation Room
July 3rd 2027
11:48 PM or 2348 Hours Military Time
President Ritt has gathered his cabinet to enjoy a last moment of peace before the launch of Operation Clean House

Imagine that all in Blue maybe.
Does a lot to set the scene and let you know what characters are involved and exactly when. You know it's right about to be the 4th of July and that the President is about to launch something with a fairly ominous name.

You could use that for any war RP or just about any dystopian RP.

Just beginning with
"President Ritt sat in the Situation Room and took a heavy breath before consulting with his cabinet"
Could have a lot of the same details added into it but would have as quick and dramatic an impact and would also require more reading.

The format of that heading, that being...

Nation
State/Territory/Province
Location
More Specific Location
Date
Time

...allows you to quickly set a very specific stage