As others have said, both sentences are grammatically fine. There are no comma splices. The more important question is the rhythm of the prose.
What's the function of punctuation? There seem to be two functions.
First, it's used to join (hyphens), separate (commas, semicolons, colons, dashes, and periods), enclose (parentheses, braces, square brackets), and show omissions of (ellipses) words, phrases, and clauses for clarity.
Second, it's used to tell the reader how the sentences should be read aloud. The joins and separations indicate stress and pauses, so it affects the rhythm of the prose.
There are many pages on the Net that talk about this (e.g., iscribe, Wikipedia, OUP [PDF file that doesn't mention how punctuation affects the sound of the language when it's read aloud]).
Fan-fiction is creative writing, which, it seems to me, ought to be about style as well as plot, character, and whatever else fan-fiction is about. Grammar generally isn't as important as style in creative writing -- but this, of course, varies with the writer, who is the primary judge of what's important in his or her work. Some writers believe that comma-spliced and run-on sentences increase the immediacy of the prose, rush the reader along, and have a positive effect. Some readers agree. I agree when it's done for dialog, but I don't like it in descriptive prose. Strictly a personal preference.
I think your girlfriend probably wants to know how her writing sounds in your head as you read it rather than whether it's grammatical. Does it make you want to continue reading her story? If yes, then what she's written is fine. If no, then what's the hang-up? If you're focusing on comma splices and other minor grammatical and punctuation issues, I think you're being too pedantic.
A couple of comments and answers talk about this sentence:
They climbed out of the carriage, and Gabriel was silent, taking in all this new information.
The authors of those comments suggested dropping the ", and" between carriage and Gabriel. That changes the rhythm of the sentence. I agree with that suggestion. The sentence is too long, the feeling is too rushed (conjunctions -- especially and -- can do that), and Gabriel needs a pause, a little time to be silent. The period after carriage gives it to him. Turning it into three sentences makes it even longer:
They climbed out of the carriage. Gabriel was silent. He was taking in all this new information.
I don't claim that this is a better way to write that first sentence, just a different way with a slightly different feeling.
Your suggestion, slightly modified, is also a possibility:
"They climbed out of the carriage. Gabriel was silent as he took in all this new information."
This isn't a pedantic suggestion.
This is a picky little point, but some of the people who comment here are professional writers who understand how important those picky little points can be.