he speaks at machine gun speed -- this is the normal way to say it, so no article because we're dealing with the abstract and uncountable noun "speed".
What about "There's an area with a forest atmosphere" -- I think we have the same situation as above -- abstract and uncountable noun.
Additional thing: What if we had a sentence such as "he speaks at a superb machine gun speed" -- do we go for "a"?
Any tips on how to navigate these waters?
Countable vs uncountable is often not a simple dichotomy. Generally, nouns are uncountable if there exists only one unambiguous instance that could be referred to. In the example, “machine gun speed” is assumed to be one single concrete speed, and everything described to be at machine gun speed has this exact same speed. (Which is of course not really exact, especially since it's used in a metaphorical way – but I'd interpret it as the fastest speed at which a human can possibly talk, perhaps unambiguous enough.)
But that doesn't mean the word speed can't be countable. The sentence could also be phrased
He speaks at such a crazy speed, almost like a machine gun.
The difference is that you're now not immediately referring to a particular speed, but first just some unusual speed (note that before the comma, it could also be an extremely slow speed!) and then narrowing it down with the gun metaphor.
“Speed” is not really abstract in either case.
On the other side, it makes sense that “forest atmosphere” is not treated as uncountable because it could plausibly refer to quite a number of different things. What does that sentence want to say?
This is an abstract use of the word “atmosphere”, though “forest atmosphere” as a whole is at most semi-abstract. Of course the word can also be countable in an concrete functions, like “the atmospheres of the planets Mars and Venus are drastically different”. It's only used uncountable when in a completely abstract meaning, like “the second restaurant had much more atmosphere than the first”. This is uncountable because it's only a broad concept... ambiguous as heck, but not because it could mean different things but because it encapsulates lots of different things that come under “atmosphere”.
While "forest atmosphere" is unclear for me, it would be possible to say "a calm atmosphere".
"Atmosphere" is a countable noun, but usually in the singular: Collins dictionary gives the example
There's still an atmosphere of great hostility and tension in the city.
Most examples of this use come with some kind of modifier to say what type of atmosphere.
There is also an uncountable sense:
The old harbour is still full of atmosphere
As a singular countable noun, it has an article "a", unless some other determiner is present.
You are right to note that many nouns which are normally uncountable, such as "speed", get used as countable nouns when used with an adjective "a great speed".
Dictionaries can help, but there is a lot of idiom, and a lot that isn't explained by "grammar", or a simple "rule".
