Technically, perhaps. But it sure is hard to read and understand.

Of course, we wouldn't use probabilistic in writing for general audiences. But I understand it's likely OK for your specific audience.

I'd argue that you don't need the word modern. Artificial intelligence and machine learning pretty much imply modern.

How about: Probabilistic forecasts based on artificial intelligence and/or machine learning are different ...

We don't use courtesy titles. I'd suggest asking the person what they prefer.

I'd definitely use the a before radio format. But I can't give a reason. I'm sure there is one. I just don't know it.

One could argue that one either way. I'd use the latter. But I think the former is fine, too.

No hyphen. We call them simply NATO members.

Yes.

No quote marks needed.

On board, and I'd rephrase: More than 500 pounds of cargo are on board the ship. Or simply ... are on the ship.

Yes as part of the committee's full name, but not on second reference. Also, we don't hyphenate vice chair.

She is the our company's representative on the AFPM Manufacturing Committee and serves as the committee’s vice chair.

This follows our style exactly: A competition for students in grades seven through 12 to propose experiments.

I would be OK with the other construction, using the numeral 7 for consistency in a construction with the hyphen.

We use the lowercase.

Our style is 1st Lt. with the period. For two, 1st Lts. is technically correct but I would rephrase:
Shawn Edgecomb and Michael Ellis, both first lieutenants, ...

We use the same style regardless of whether the person now holds it or used to hold it.

As for whether it's a title (for which we use uppercase) or a job description (lowercase), that depends on how the organization views it. See this part of the titles entry:

A final determination on whether a title is formal or occupational depends on the practice of the governmental or private organization that confers it. If there is doubt about the status of a title and the practice of the organization cannot be determined, use a construction that sets the name or the title off with commas.

That's correct.

The plural.

We wouldn't use the tilde. Some readers don't know what it means, for one thing. And yes, some are likely to just ignore it and think you mean 123%, no approximately about it. Why not just use the word? 

Is, since it's ongoing until this summer, right?

That's unless you want to make a particular point that a lot of work had been done by April. In that case:
The final work was well underway in April and should be completed this summer.

We don't have a style for that. I'd use uppercase for each word.

We use a.m. and p.m. for digital as well as print. Our stories are published simutaneously to both print and digital. You could choose to use AM and PM, of course.

I'd hyphenate it. 

We deleted the entry. 

It should be data set. We'll make the change in News Values and Principles. Thanks for noting it.

A two-day outage, in our style.

I would much rather read for roughly 48 hours (more conversational) than for roughly a 48-hour period (very stilted).

Could you give me some examples?