1. Would you be able to discern whether or no the tongue was genuinely non-terrestrial and if so how?
Your scenario suggests that the sounds and perhaps general structure of the language is similar to our own. Therefore, it is possible that there is no way from the signal itself to determine that it is not made by humans. Perhaps these aliens are humanlike, at least in their speech abilities. There is no way to determine that a language is from earth unless the language shows non-humanlike properties. It certainly might. The easiest test would be for sounds that can't be produced by humans, although from the signal alone that could be challenging. Beyond that, theories of "Universal Grammar" (among HUMAN languages) would suggest some commonalities, but they are hypotheses about observed human languages, not predictions about what is non-human. So that would be a longshot as a test. The only other way would be for someone who knows a lot about many languages to figure out it just doesn't seem to belong to any groups, by elimination. But there are 6,000 or so languages today, so full elimination would be impossible.
2. Would you, in time, be able to translate said tongue and if so how?
Major breakthroughs in translation involve some kind of key to the meaning. The Rosetta stone allowed translation of Ancient Egyptian by having a Greek parallel text. Other cases where a historical relationship between two languages has been identified have been solved by comparison and guessing. A lot can be guessed, but there must be some kind of hint as to the meaning. Another way is through observation of correlated behavior. Take a look at this:
https://www.youtube.com/watch?v=sYpWp7g7XWUBased on ONLY the sound itself, I don't think we could get too far. I don't know if this situation has ever existed for linguists in real life, but it has existed with writing systems. And in those cases it was almost impossible without some clues and context. That's when the breakthroughs happen.
Based on the signal alone, I think we could do some basic analysis, finding common words/sound groups, figuring out some basic grammatical forms, etc. But it would be entirely meaningless without some way to translate a few of the words at least. If it was similar enough to human languages here we might with enough data be able to make some guesses and start to fill in some blanks, but there's no reason to assume it would be. Do they have verbs? Proper names? Etc. In the best case we might be able to make a full logical grammatical description of the language with no actual understanding of what any of the words mean or why they are used-- these words get this ending, these get that one, and so forth. So we could generate random (nonsense) sentences in the language, but not actually work out the meaning.
Regarding context, also see the following:
https://www.youtube.com/watch?v=y1kXCh496U03. If translation were not possible, would an attempt to communicate with the sender, presuming no common language, by radio transmission enable translation and if so how?
Issues with the speed of light might make this very hard. But yes, if enough back and forth communication were possible, eventually the interaction could provide enough of a clue to the meaning. See the video above.
