3 completely different words... meg = és = and (OR meg = plus )
we use "hanem" when we say that something is not true, but another thing is true. (Hard to explain this, let me some examples). We don't go to the cinema, but we go to the circus. = Nem a moziba megyünk, hanem a cirkuszba. You should not capture the rock, you should capture the queen! = Nem a bástyát kellene leütnöd, hanem a vezért! (Instead of: Nem a bástyát kellene leütnöd, a vezért kellene leütnöd!) There were five elephants in the zoo, not four. = (Öt elefánt volt az állatkertben, nem négy.) OR Nem négy elefánt volt az állatkertben, hanem öt.
If after "hanem" the verb is the same, you don't need to use the verb again.
We use "pedig" when:
- we give an advice :
You: I don't want to go to the cinema. Me: You should go to the cinema. = Pedig el kellene menned a moziba.
- we knew something wrong:
You: I was working last Friday. Me: I thought you were on holiday. = Pedig azt hittem/gondoltam szabadságon vagy.
- we wanted something but we couldn't do it
It would be good if we could go the cinema! = Pedig de jó lett volna elmenni a moziba!
I hope I could help you. It's not sure, I told you all when we use these, but suddenly I don't rembember more examples.