Bike makers tend to design frames (or choose forks for a frame) with a particular fork rake in mind. Changing the rake can have ill effects on how a bike handles that maybe the manufacturer did not plan for given the rake thay had in mind when they designed the bike. It's just like how using a forward seatpost (and drastically changing the effective seat angle of the frame) can have negative effects on the ride quality and handling of some frames. So if you have a bike that was designed with ride quality and handling in mind, and you want retain as much of those qualities as possible, I'd recommend using the same rake in any new fork you may buy for the frame.

As for how rake affects trail, it's a little counter intuitive. A smaller rake increases trail while a larger rake decreases it. So in general terms increasing the rake often makes handling a bit "twitchier".

OK, I'll add an edit. These sorts of changes don't only mean the bike becomes more or less twitchy. It could also introduce some strange behavior like speed wobble (or death wobble) at high speeds. You really don't know until you try. You do know though that these things have likely been addressed in the factory setups for bikes from quality manufacturers.