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A link to a calculator is posted below. IMO, people tend to greatly overstate the effect of minor changes (40mm vs. 43mm) in fork rake.
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.
You really have to watch it when messing with the fork on your bike. I am now convinced that possibly a person who knows frame building (who is smarter than I, for certain) is the only one who can help make a decision for your new fork. They can help decipher some of the harder elements of making the correct choice on your fork.
Depends. :-) Bunnyman's point about stack height is that if the new fork winds up lowering (for example) the head tube a bit, that increases head tube angle, which affects trail, which affects handling -- so rake should be adjusted to compensate in such a case. What you want is a fork that holds the wheel in the same position relative to the head tube, which means two dimensions need to be correct: the rake, and the dimension along the head tube axis from the rake measurement point (ie, opposite the dropout) to whatever your reference point is that corresponds to a fixed point on the head tube. The latter dimension is not as critical, but can be significant.