Why didn't the Indominus Rex eat or kill the Velociraptors?

I think the link from Napoleon Wilson provides valuable insight. Another consideration is the Indominus' intelligence. As it was already mentioned the canon establishes the Velociraptor as an intelligent creature that communicates and coordinates to attack prey, the T-Rex sees no such treatment. In the first film these two species are juxtaposed with one another to demonstrate the raw intelligence of the raptor which infers the T-Rex is in some way intellectually inferior. The T-Rex is a doer, not a thinker; brute not brain.

The Indominus is also hyper intelligent, perhaps moreso than the raptors themselves. The creature could know that the raptors are more able and more willing to follow commands, where the T-Rex might not listen or might not even be at the capacity to communicate with it.

Why didn't the Indominus Rex eat the velociraptors?

This could just be the relative levels of intelligence between the raptors and the T-Rex, as Josh said, but I think there's a bit more to it than that. Not only are they shown to be highly intelligent, but they're shown to be social pack creatures. They live and hunt and work together, they're not intended to be alone.

In addition to that, the velociraptors in Jurassic World are B, C and D; Owen is/was the alpha (A). They're already primed to be followers, not leaders, so they'll readily submit to the Indominus Rex, which is intelligent enough to realise their potential as allies rather than food (or sport).

Also, given the vast difference in size, the velociraptors aren't going to be depriving the Indominus Rex of food to a huge extent. It's already killing far more than it needs to in order to survive, so the small amount that the raptors will consume won't be noticed.

Why didn't it try to ally with the Tyrannosaurus Rex?

Again, this could just be the relative levels of intelligence. However, even if they're capable of communicating, the T-Rex is a much larger threat to the Indominus Rex (as seen at the end of the movie), and is not a social pack creature. It's not going to just readily submit to be a follower; there's going to be competition primarily for dominance, but also for food. Best to just eliminate the competition straight away.

Which brings us to...

Why did the Indominus Rex eat its sibling?

I've kind of covered all of the likely reasons already, but I'll list them again:

Competition: Its sibling will be competing for dominance and for food. Another Indominus Rex is by far the largest threat to the Indominus Rex out of all the dinosaurs at Jurassic World.

Food: Rommel suggested in his answer that it may have just been hunger. I think this is the least likely explanation, or at least its not the primary motivation, but it is a possibility. The amount the dinosaurs are fed isn't shown in the movies, but from what we do see it didn't really seem like they were fed that much considering their size.

Sport: Owen explicitly states that, once the Indominus Rex has escaped from its enclosure, it is killing for sport. There's no reason to think that wouldn't have started earlier in its development, and when you have two creatures that kill in large part just because they enjoy it sharing the same enclosed space, one of them is going to end up dead eventually.

Since it was a hybrid and was made of all other types of dinosaur such as a T-rex and velociraptor it wouldn't eat the raptors. When she ate her sibling it could've been hunger.

Another reason the indominus Rex didn't kill the velociraptors was because they would do the work for her. She has intelligence of a human and to know when a group of the same species are together, that means that they will most likely have some sort of monarchy or a leader/ alpha who is in charge. She knew that if she can get on the raptors good side then she might be able to lead them. For using the raptors to get rid of the humans, was her plan. She wasn't scared because earlier in the movie she fought numerous guys with teasers and highly equipped guns by herself. She just probably wanted to save her energy or make it no problem for her.