There is no way to speed it up because it's all managed by the server. This game is actually made in a smarter way that Crush Crush which does the stupidest thing: trusting the player. Players often try to cheat in some way when they are trusted by the game, so them not trusting the player is a smart choice... Only smart choice they made though.
They stay after reset, which has been answered in this topic already... :P
There's currently 3 tiers of girls (5 girls per tier), each with a large increase of difficulty. They are adding 2 more, for a total of 25 girls.