Trying to start IntelliJ IDEA 13 under Yosemite leads to a popup window and tells you to use Java6. There is a simple workaround to prevent this problem by changing the Info.plist inside the IntelliJ application package. Search for the following xml code and replace the 1.6* by the java version you are running.
According to this support article it is not advised by JetBrains to do so. Do the change on own risk. I am using IDEA 13.x with Java 1.8 and Yosemite mainly for JavaEE development and do not suffer from the listed problems. At least I do not recognize e.g. the alt key problem. And the big ones like crashes do not occur.