Thank you for explanations.

You can not use these words interchangeably. weer = again nog = can mean 'still' (ik wacht nog = I'm still waiting), but in your sentence it means 'another'. een andere = a different one, another one

You could change 'weer' and 'nog' in the first sentence but the meaning would be slightly different. Hebben we morgen weer les van u -> assuming you allready had one lesson before Hebben we morgen nog les van u -> assuming the period of lessons would end soon The difference between the words WEER, NOG and 'andere' is that Andere is an adjective, which allways accompanies another noun (Adjectives are words that are used to describe or modify nouns or pronouns). 'Weer' and 'Nog' are adverbs. You can say : Ik heb nog een 'andere' les for exemple. Andere modifies the word 'les' (noun).