A note before I answer:
I generally would use "demo" as "but", and I would translate "ga" between two clauses as "even though".
1) Watashi wa machimashita ga, kare wa kimasen deshita.
Even though I waited, he didn't come.
2) Kinō gakusei wa Furansugo o benkyō shimashita ga, kyō daigaku e ikimasen deshita.
Even though the students studied French yesterday, there wasn't any school today ("they didn't go to school today")
3) Haha Chūgokugo o hanashimashita ga, kakimasen deshita.
Even though my mother (could) speak Chinese, she (could)n't write (it).
4) Ima hon o yomitai desu ga, tomodachi wa yomimasu.
Even though I want to read a book right now, my friend reads it. (is reading would be yondemasu or more correctly yonde imasu)
5) Inu wa neko o mimashita ga, neko wa inu o mimasen deshita.
Even though the dog saw the cat, the cat didn't see the dog.
1) You don't sleep at the cinema but you read a magazine and a book.
Anata wa eigakan de nemasen ga, magajin to hon wo yomimasu.
(as I noted before, I would use "demo")
2) My friend and I watch a film at school.
Boku wa gakkou de tomodachi to eiga wo mimasu.
(eargh... I forget exact sentence order sometimes. i think it's boku-ha gakkou-de tomodachi-to instead of boku-wa tomodachi-to gakkou-de)
3) Mother taught at the university and the school.
Okaasan wa daigaku to gakkou de kangaemashita.
4) I didn't go by bus to work but I went with a friend by car.
Boku wa basu de shigoto ni ikimasen deshita ga (it's a whole lot more convenient to say 'ikanakatta ga', but I assume for right now we should just use formal), tomodachi to kuruma de ikimashita.
5) I didn't write the letter to my boyfriend but I wrote to you and a friend.
Boku wa koibito ni tegami wo kakimasen deshita (kakanakatta... yep...)