• Remotely, according to the oxford dictionary (in this context), means in the slightest degree. So I would translate it as "Si le reste du monde ressemble même un peu à ce qu'on vient de voir en ville, j'suis sûr que oui." Though of course I can't guarantee this is actual French 8D

• For the infinitive or -ing form, it's tricky, because in most cases there is only a very slight difference between the two forms. Here, I would use the infinitive (to open), because it suggests that Unknown made an attempt but didn't succeed. Honestly though, they both fit. It depends what her intention was.

• stair = you should either use the plural (stairs) for this word, because "a stair" doesn't really exist (a stairway does though, and so do the stairs) or, I think the word you were originally looking for here, the steps.

• Yes, stair all by itself would be in the context of large stairs. Like... imagine if you're in a house in front of the stairs, and you notice a stair is broken (out of the many there). For the stairs in front of a house or when it's only a few, you'd say steps indeed, that's it, you're absolutely right \o/

• cozy coach = Unless she found a human being in the cabin, like a football coach on a school's gym team, I think the word you meant was couch 8D

Just repeating what I said in Skype so you can keep track of it 8D

• Hold our position = So like I said, I think it's totally okay since you speak of them as a team in this context
• She whistled an admiring whistling! = whistling is an adjective and you used it as a noun here, so that's a bit weird. You can just say: "She whistled with admiration"

• She kept her search up = just "She kept searching" is fine (though you have to add a comma or a while in between searching and ignoring)
• pretty clear = clearly here, as an adverb, since it stands with the verb 'to hear'

• she find herself not so eager = This is a very strange construction in English. If you want to keep the construction, I'd change it to "She found herself not to be so eager to [...]", which would be syntactically correct, but it would still be more natural to say something like: "She wasn't eager to go back [...]"
• she sort of like = liked
• Real sleep over and quiet life = I didn't get this D:

• Real sleep over and quiet life = Une grasse matinée is to sleep late or to sleep in. So it would have to be: Sleeping late and having a quiet life.

• bag of crisps = Note: not wrong, but British ! In American English it's chips. (Which means fries in British English.) Aaaah, English 8D But since Unknown is like a very cool mix of all kinds of English varieties, it's totally okay. Her English is... unknown after all 8) Lame puns.
• Is there any Mars bars? = are there, since it's plural °^°