Question one: is he getting fired or has he resigned?
Question two: will he do interviews/write a book/otherwise go public in the near future about the White House dumpster fire?
My guesses: fired, yes, within three weeks.
Rosenstein is going to the White House, Trump is not at the White House, so…fired. Trump never does it personally.
It’s the Chief of Staff’s job to do it. It’s not that Trump doesn’t want to - he probably doesn’t but it’s irrelevant. The Chief of Staff handles all personnel matters.
They will claim he has resigned and he will dispute it.
and the chaos will distract from problems with the Kavanaugh confirmation.
He always looked to me like a man who did not spend enough time with his family.
The start of a slow motion Saturday Night Massacre. Will Donald find someone with the scruples of Robert Bork to fire Mueller?
Trump, on the other hand, is a man who has spent far too much time employing family in roles that they are not competent to hold. When all of your children are Fredo, you should really outsource more often.
Stranger
In the GOP? You can find someone with the scruples of Charles Manson.
Kavanaugh might be available. 
This slow motion massacre actually started on May 9, 2017. This one is moving really slowly, but it’s heading toward a similar end, I think.
Your post reminds me of when former congressman/convict Jim Trafficant was chastised for comparing the IRS to a bunch of prostitutes during a speech on the floor of the House, and then he quickly apologized to the prostitutes of America.
I am starting to think we have a Schrödinger’s Rosenstein - Fired and Resigned at the same time.
This
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He will not resign - he will be fired.
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If the White House tries making the claim that yeah, no, the guy totally resigned, I imagine that Rosenstein will publicly, and forcefully, refute it. But other than that, I don’t imagine him doing many (any?) interviews or media appearances anytime soon.
Nothing happening today. Trump meeting with Rosenstein Thursday.
Same day as the Kavanaugh hearing.
Assuming that Rosenstein is out of a job one way or another, what next? Can whoever takes his spot simply demand to know everything that Muller has and promptly report it to Trump?
Fired, yes, ??.
I’ll say within 2 months. If he takes closer to a year, it means he’s pumping up sales of his book. My WAG is that he won’t optimize around that, but who knows?
What Trump might do is wait until the election is over and then clean house at Justice/FBI–starting with Sessions, Rosenstein, Mueller…
Don’t forget the other things on Trump’s 2019 to-do list: get Mexico to pay for the wall, find Obama’s real birth certificate, re-hire Omorosa (he had no idea that John Kelly was firing her!), and lose ten pounds.