I am having trouble translating the following sentence:
スーザンは一人で淋しがっています。
I can't determine whether it means:
From my understanding of ~がっています is that it means "shows signs of~"
So the sentence in my mind should mean "Susan seems lonely by herself."
Let's go by exclusion.
We can pretty much exclude 2.: it implies a comparison among other people, and there is nothing here that seems to suggest that (だけ、しか。。ない, etc). Unless, maybe I should add, in this case the は is used as contrast particle, which implies that the speaker "knows" that she feels lonely by herself (but others don't).
Number 1 and 3 are pretty similar in English, and could both work in this case. 淋しがる is an intransitive verb meaning "to miss someone / to feel lonely".
The -がる construction with いーadjectives turns the word from an adjective to a verb meaning feeling like or looking like (as you say) that adjective. In this case, it just means "feeling lonely". For more about -garu, see here for example. There is actually also an example very similar to yours.
So to recap, Susan feels lonely by herself, seems the most appropriate translation to me.
However, I would like to point out also another option.
Do you know that two sentences can be connected by the "pre-masu" form of a verb? See this question for example. Well it works in the same way with です --＞ で.
Hence, in this case, the sentence:
スーザンは一人で淋しがっています。
could also be:
Susan is alone and (because of that) she feels lonely.
PS. I also asked a native speaker about this sentence and she said it could be both, either 1. or my last example.
スーザンは一人で淋しがっています。
I think you can apply the sentence #1, #2, #3. I analyze the sentence as the following
I think these 3 sentence describes she is showing the sign of ~.
