- Is ねぇ a negative particle here (shortened from ない) – or does the sentence mean something else entirely? If yes, how do you tell?
First, notice that I made a small change to your question (added ぇ). You are correct to understand this as a negative. This happens a lot, especially in anime. The first thing that comes to mind is Goku, in Dragon Ball Z. He uses this form a lot.
There's a bigger picture here, and it happens with adjectives that end with い。 As an example, I'll use すごい and やばい。
すごい！ー＞ すげぇ！
やばい！ー＞ やべぇ！
You'll notice that it's the same formation with ない as well.
Occasionally, this structure is used because there is more feeling behind what is being said. In other words, you're showing more emotion. Imagine that you're going on vacation to a dangerous place. Not knowing the severity, a good response from a friend would be やばい, but if you said you were going to North Korea, you would get やべぇ as a response.
Using this structure to show more emotion isn't always the case, as some people just use it to be super casual too. Like I said before Goku in Dragon Ball Z is a good example of this, especially when he's talking to his wife or Kame-san.
Keep in mind that this is considered slang, so I would recommend not using this conjugation in formal situations. You can use it with your friends, or in informal environments without offending people, or sounding too casual.
See this answer for more information about this structure and its formation.
How do you tell?
It's quite easy actually. ない becomes ねぇ or ねー, and the rest of the verb conjugation is the exact same.
- Does ことも have the same meaning as explained in the answer here: Combination of verb + ことも
Yes, with one small difference
こと in the question is the noun form. It is literally translated as things. こと in this case is a nominalizer. It turns 'verb', to 'the thing of verbing'. For example:
歩く (to walk)
歩くこと (the thing of walking)(this is a noun)
This difference in こと, however does not change how も affects the sentence.
も in this case is just as explained in that answer. To quote the author of that answer: The 「も」 simply suggests that there are other things (besides what the listener wants to know**) that the speaker will be explaining/teaching for the listener later on.
**I would also add that in this case, this includes things that have not been listed yet. In short, we have non-exhaustive list here.
Finally, I'll end with a translation (you pretty much had it.)
この国じゃ、肌が黒いってだけで、自由に呼吸することも、歩き回ることもできねぇ
In this country, you are not free to do breathe, walk around, etcetera, just because your skin is black.
Note: ... you are not free to ... should literally be translated to ... you cannot freely ... I changed it to be more natural in English.
