Here are my attempts. They are sometimes not very
literal. If they differ from yours, it doesn't mean yours are
wrong.
1) J'ai rencontré Brandon hier au cinéma.
I came across/ran across Brandon yesterday at the cinema.
I ran into Brandon at the movies yesterday.
(I wouldn't say came across. I use that for inanimate objects.)
(English usually mentions place before time.)
2) Retrouvons-nous à 10h00 devant la bibliothèque.
Let’s meet / meet up at 10 o’clock in front of the library.
Let's get together in front of the library at 10 o'clock.
3) Tu as entendu ce bruit? Je crois quequelqu'un s'est fait renverser.
Have you heard tha tnoise? I think that somebody has been knocked over.
Did you hear that noise? It sounds like somebody got run over. (???)
(renverser can refer to a car accident, can't it?)
4) Je n'ai plus d'argent. Pourrais tu m'en prêter?
I haven’t got any money left / I'm running out of money. Would / Could you lend me some?
I've run out of money. Can you lend me some?
(I wouldn't say running out.)
5) Je veux bien te déposer chez Sonya mais alors on partage les frais.
I’m ready / willing to / I agree to drop you off at Sonya’s but then we share out / split up the expenses.
I don't mind dropping you off at Sonya's as long as we share the expenses.
I'd be glad to drop you off at Sonya's, but in that case we should share the expenses.
(I wouldn't say share out, just share.)
6) Je ne pourrai pas venir ce soir, j'ai un rendez-vous avec Tash.
I
won’t be able to come round tonight / to make it this evening, I’ve got
an appointment with Tash / I've arranged to meet with Tash.
I can't come over tonight. I'm meeting Tash.
(come round is more British, so I don't use that.)
7) J'ai rendez-vous chez le docteur à 13h00, mais on peut mettre quelque chose au point après!
I have an appointment at the doctor’s at 1 pm, but we can work something out / fix something up later on.
I have a doctor's appointment at 1 o'clock, but we can work something out later.
(I wouldn't use fix up.)
8) Dans quel bâtiment est notre partiel? Je n'en sais rien, il faut que je me renseigne.
In which building do we have to write/sit our exam? I have no idea, I've got to find out.
In which building do we take the exam? I have no idea. I (still) have to find out.
9) J'essaie de trouver une solution à ce problème.
I am trying to figure out this problem / find out a solution to this problem.
I'm trying to solve this problem. / I'm working on this problem.
(I wouldn't use find out a solution, just find.)
10) Je n'ai rien à voir avec cette histoire! Réglez ce problème entre vous!
I have nothing to do with that story! Just settle the problem yourselves / Sort the problem out by yourselves.
I've got nothing to do with it! Work it out for yourselves!
(story doesn't fit this context.)
11) Ils ont inventé une histoire invraisemblable.
They have made up an incredible story.
They made up an implausible story.
12) Quand il est enfin arrivé à la soirée, la plupart de ses amis étaient déjà partis.
When he finally showed/turned up / loomed up (?) at the party, most of the guests had already left.
By the time he finally [showed up at / made it to] the party, most of his friends had already left. (not loomed)
13) Ce n'est pas facile de se tenir au courant de tout ce qui est publié.
It’s not easy to keep up with everything that is published.
(Same.)
14) Un week-end à la mer ou une soirée à l'opéra ? A toi de décider.
A weekend by the sea or an evening/night at the opera? It is up to you.
A weekend at the beach or an evening at the opera? It's up to you.
15) Il y avait un énorme fatras à nettoyer après le départ des invités.
There was an awful mess to tidy/clean/clear up after the guests had left / after the party (?).
There was a huge mess to clean up after the guests left.
CJ