Why not "Mera"?
If you read the Tips and Tricks section of this lesson (not currently available on mobile app, only website), it disrespectful to use the singular form to address family elders, hence 'mere' is used.
Why मेरे before दादा?
The same reason why there's "my" before grandfather in the English sentence. You could remove the My in the same way that you could also remove "mere".
Why "mere dost" and not "apni dost"?
Because apne would relate dost back to the grandfather and not to you. At least that's my understanding.
Shouldn't the oblique case be used for "my friend" here?
no, because there is no postposition after दोस्त.
हैं is a verb and मेरे is an adjective
"Father's father" should be an accepted translation of dada. It is a specific grandpa.
A friend of mine told me that granfather has to be named "dada gi" in a polite way.
But not in Duolingo!
But I don't know why it says दादा
What about you?
Is it plural for politeness? :o