Is it from the Sunnah to say aameen to the dua of the Imaam (after prayer)? What about the duas that are made randomly- should we say aameen only after our own duas? Also, what should we reply to someone who makes dua for us?

The dua that is made in a loud voice by an Imaam after congregational prayer is bid'ah. So there is no need to say "Aameen" to that type of dua. However, in instances where it is Sunnah for the Imam to make dua like in Witr prayer in congregation, etc, you can say, "Aameen".

You  can  say aameen if  a  person makes a general dua or if someone makes dua  for you; for example if you do someone  a favor  and they make dua for you, there is  no  evidence to  say that saying , "Aameen" in such  cases  is wrong or  haraam.

As  for the  question of saying, "Aameen" to  your  own dua, I have not come  across evidence to  support that or to suggest that doing so is Sunnah.