Could someone tell me when to use hâlâ or daha? Those words confuse me sometimes.
Is the use of hâlâ / daha in the following sentences correct?

Gelecek sene Brüksel'de hâlâ öğretecek mi?

Will he still be teaching in Brussels next year?

Daha gelmedi mi?

Hasn't she arrived yet?

Sağol

Yes

'Hâlâ' and 'daha' are correctly placed in these sentences. On the other hand "öğretecek mi?" isn't suitable here. Instead we use "ders verecek mi?"

Öğretmek isn't refering to a teacher's job. It is refering to teaching as an action which isn't necessarily related to teachers. Öğretmek means "to teach a certain thing".

Example:
Bana yemek yapmasını öğretir misin?
Can you teach me how to cook?

Thanks!

But I have another question
If I wanted to say "He is still here", do I say "O hâlâ buradadır" or "O daha buradadır"? I really don't see the shade of meaning here.. I have the feeling that one of those sentences could mean "He is already here" as well.. Don't know which one though..

"O hala burada" without the -dir is better. We use the -dir usually in statements about facts. No, none of them means "he is already here". "O daha gitmedi" is alright but I wouldnt use "O daha burada" which sounds not as good as "O hala burada".

Example:
"Kuşların iki kanadı vardır."
Birds have two wings.

Hala is prefered when something lasts longer than you thought or than it is supposed to be. It is close to the word 'still'. Daha is more indifferent and is close to the meaning 'yet'.
Example:
"Daha gelmedi" : He hasn't come yet.
"Hala gelmedi" : He still didn't come.

Thanks, it is getting clearer now.