Is there a point to interacting with Pokemon in your lobby/city area?

Solution 1:

If you continue to interact with a Pokemon (talking and jumping) you will increase its "affection" for you, ending with an happy face with hearts for eyes ♥_♥, as you wrote.
You can see the exact moment when this happens, that will trigger your Mii who runs towards you with orange blinking lines around his head.

If you speak to the Pokemon again sometimes he will start to follow you for a while. After that the Pokemon will become "offended" showing a face like u_u.

I don't know what this means. I've tried to start a mission with a Pokemon following me, but nothing happened.