In bee breeding, when you discover a new species, your number one goal is to get a pure pair - that is, a pure princess and a pure drone. Pure princesses for forest, meadows, etc. can come from hives, but they CAN also be bred. Imperial bees, for example, cannot be found in the wild. The only way to get an imperial princess is to breed one yourself.
This generally begins by getting lucky when breeding noble and majestic. You might get, like a majestic-imperial drone or something. You usually get noble-majestic hybrids, but you can drastically increase your chances of getting mutations by using ExtraBees soul frames (you'll need a squeezer and a carpenter for those, as well as a source of seeds and a source of MJ power). So, it's a little bit of gambling. Then, one day, you'll get lucky and get a majestic-imperial princess (or noble-imperial, or something). Then, you take one of those imperial drones and mix it with an imperial princess, and try and get a pure princess. Hopefully that answers question 3.
Question 2: Yes, it is possible (although very rare) to get royal jelly through hybrid queens, like a noble-imperial queen. This is not reliable though.
Question 1: Yes. See below.
To better understand how bee breeding works and how traits get passed on, you need to understand your beealyzer. (If you have not yet crafted a beealyzer, this is a must). If you look in your beealyzer, you will see two columns. The left column is the active trait, and the right column is the passive trait. So, for a noble-imperial hybrid, it technically is a noble bee, but it still has a bit of imperial genes it can pass on to future generations when bred with another bee. This works for other traits too. For example, let's consider the nocturnal trait. Rocky bees have this. Forest bees do not. So, suppose you mix a rocky with a forest, and you manage to mutate a pure common princess. You look in your beealyzer on page two, and see nocturnal with a NO and then a YES. This bee isn't nocturnal, but it's future offspring might be if you mix this common princess with another bee that has the nocturnal trait. You just need to get lucky. You can also see what products a queen will produce by putting it into the beealyzer.
NOTE: Once you get more advanced into bees, you can use some advanced ExtraBees machines to create species serums. So you can take your imperial drones, extract imperial species serum from them, and use it to turn other princesses into imperials. You can actually create a serum for any trait you want, like 4 offspring, or nocturnal, or cave, or anything like that (not products, though). If you play on a server, you should see if anybody has already built these machines.
Hope this is helpful! Please feel free to ask any more questions.