Well if you're looking for some thoughts on the possible ideas bit; I'll give it a go.
Adopting lost Pokémon
It depends on how you execute this. Perhaps important characters may lose their Pokémon and you'll have a chance to adopt them... I'm not sure, this is pretty vague.
Meet your father
This sounds interesting if you can develop it into the plot. But for you to just randomly meet him after five years of him being disappeared, then it just doesn't sound worth adding in.
Other People on the same mission
You got a 'yes' from me on this one. Constant characters are always a nice thing to have around you as a player, especially if you can compare yourself to them, and they have some decent character growth.
Day and Night system
My personal opinion is that you shouldn't bother. It doesn't add anything spectacular to game play, nor does not having one subtract anything.