(1)
Arimasu is perfectly fine here. The problem rather is the expression no naka. It means "inside of". What you want to say here is "Toulouse is in Midi-Pyrénées", but not "Toulouse is inside of Midi-Pyrénées". Therefore, what you should say in Japanese is:

Toulouse (a town) is in Midi-Pyrénées (a region)
Toulouse wa Midi-Pyrénées ni arimasu.


(2)
I think the expression you want to use here is benri, which is a na-adjective and it means "convenient". Then I would say, benrina tokoro desu which literally means, "is a convenient place". The whole sentence will translate into something like, "Midi-Pyrénées is conveniently located."

Midi-Pyrénées is well located in France.
Midi-Pyrénées wa benrina tokoro desu.


(3)
In Japanese, whenever you count something, you have to use a counter. An equivalent of counter in English is "glass" in "a glass of wine", or "loaf" in "a loaf of bread". In English, you only use these counters for certain "mass nouns", but in Japanese, you have to use a counter for everything. In the case of metro lines, you would use the counter hon.

There are 2 metro lines.
Chikatetsu ga nihon arimasu.


(4)
Again, you have to use the right counter. To count people, use nin.

Another thing you have to remember is that you cannot use arimasu when the subject is a person or an animal. If you have a person or an animal as the subject of a sentence, you must use imasu instead of arimasu.

You can use either imasu ("there are") or sundeimasu ("live") in this sentence. It's up to you. However, the verb sundeimasu is a bit advanced. So if you are a beginner student, I would actually encourage you to use imasu.

There is about 430000 people living in Toulouse.
Toulouse ni wa yaku 430000nin no hito ga {imasu/sundeimasu}.


(5)
Almost perfect. Just delete the particle ga!

There are 50km between Toulouse and Revel (a town)
Revel kara Toulouse made 50-kiro arimasu.

Good luck on your school project!

>Giya-san to marry him.
>Kyou wa, Jibi-san no mezurashii doyobi desu, Giya-san ni puropouzu 

>shitai desu kara.

The word mezurashii means "rare". To me, "rare saturday" sounds odd. I also notice that your English uses negation; i.e. "not an ordinary Saturday". I think you should use negation in Japanese too; i.e. use the negative version of desu. For "ordinary", just say futsuu (means "normal"). Futsuu is a noun, so make sure that you use the particle no when you try to say "normal Saturday". 

Also, you don't need to try saying a long and complicated sentence using "because" at this point. (You will need to alter the word order.) Simply say, "Today is not a normal Saturday. He wants to ask Giya-san to marry him."

I don't know how you were instructed in your class, but normally, when you say some third person "wants to do something", we use the expression -shitagatte imasu instead of -shitai desu. In your case the subject is "he", so you are supposed to use -shitagatte imasu.


>They've been dating for 8 years now
>Jibi-san to Giya-san wa 8nenkan tsukiatte imasu.

This one is good.


>He has a rendez-vous tonight with her in a chic restaurant
>Konban, kanojo to koukyuuna resutoran de randebuu ga imasu.

We don't use "randebu" in Japanese. Just use the regular verb aimasu, which means "to meet".


>He will then prepare himself for the rendez-vous
>Nazebaraba, kare wa randebuu no junbi o shimasu

Do not use nazenaraba, unless you are writing a dissertation. It means "because" but it sounds way too formal. 

Again, don't use "randebu" because we don't say it in Japanese.


>Jibi-san will join Yoko-san (in order to go somewhere together)
>Jibi-san wa Yoko-san o mitsukemasu.

Mitsukemasu means "to find". I don't think this is what you want to say here. Simply use the verb aimasu.


>Jibi-san is looking at the rings while listening to Yoko's advices
>Jibi-san wa Yoko-san no adobaisu o kiki shinagara, kon'yakuyubiwa o >mitteimasu.

kiki shinagara ---> kikinagara
mitteimasu --> miteimasu


>Also, how to express a feeling? For example:
>"He finds the ring beautiful"
>How to say "to find something" (speaking of a feeling, not actually >finding it)
>(My english may not be quite exact on the explanation above ^)

The construction you are talking about doesn't really exist in Japanese. If you want to say something like it, just say, "He thinks that..."
That would be, "[so and so] to omoimasu".


>Jewelry: Housoku
>Jewel: Houseki
>Architect: Kenchikuka

Both "jewelry" and "jewel" are houseki, but we also say juerii (i.e. katakana word).