When 「」 is used to quote, are the words contained always literally what they say, or are they paraphrasing? For example, in a sentence such as 「助けて」と叫びながら走っていた人が多かった, does it exclude people from saying variations such as 「誰か助けて」 and imply that 「助けて」 is the only thing that they said, or are they just giving the general idea of what was saying? Another example sentence I'm having trouble with is 「これって何」と思いながらプレゼントを開封した. The time it takes to think a phrase is short compared to the time it takes to open something, so is 「これって何」 the only thing they think or is it just given as a general idea of what is being thought?
No, they are not. The content inside 「 」 is often not the exact same as what was actually said. There exist a few patterns when it is not.
1) Summarized statement:
When the author thinks that the actual statement is too long and/or it contains unnecessary parts for the reader, the author may trim it a little without changing the meaning or nuance of the original statement.
2) Translated dialectal statement:
When the original statement was made in a dialect and the author feels it would be better to "translate" it to standard Japanese for easier comprehension for the readers, the author would sometimes make the alterations.
I would not include translating from another language in this category because that is a totally different phenomenon.
Native speakers quite often place words and phrases in 「 」 for the simple purpose of emphasizing them or making them stand out "physically" to catch the reader's attention (even if no one actually said those words).
Technically speaking, this use of 「 」 is rather questionable, but many people do it including myself.
Finally, I did not mention placing titles in 「 」 because that is only "legal" officially.
The simple answer is yes.
Of course, it can sometimes depend on the situation being described, or the author's intent, or on the reader's imagination. But consider the「」quotes as being analogous to the "" quotes in English.
There were lots of people running and shouting, "Help!"
Read the passage in English and ask yourself the same question. Does "Help!" just mean everyone was saying "Help" or could it mean that maybe some people said "Help me"? That could be up to the reader's imagination, and surely we can imagine that some people might have shouted "Help me" or some similar variation.
Same with your other example. We know that the person opening the present certainly thought 「これって何」because the sentence explicitly told us to. But as readers, we can imagine that there may also be other thoughts running through the person's head. Maybe they are guessing what the present might be even as they open it.
So just like in English, we have to assume that things in quotes are literally what is being said. Sure, we can imagine that the character might be also thinking something else. Or that in a crowd of people shouting 「助けて」some of them may be shouting 「誰か助けて」or「逃げろ」or something similar. As readers, we are usually free to guess or imagine whatever we want. But if you have to look at things in terms of black-and-white, then in that situation we can't allow ourselves to imagine anything other than what is written. And so we must conclude that what is being thought or said is only what is literally written in the 「」quotes.