New kitten and Tikibird - Can they coexist?

I have a 3 year old quaker parrot named Tiki. We have had him since he was 2 months old. He's extremely loud and can be very irritating - but we love him dearly. Tiki is quite attached to us as we are to him and he has free roam of the house. He follows us from room to room and is only in his cage at bedtime or whenever he wishes to be. Here's our problem........a stray kitten found us last week.

Her name is Sunny. I take care of a feral mother cat and her two 2 year old babies. I thought that since Blondie was such a good mom that she'd take care of Sunny. None of our babies wanted anything to do with her. She's now an inside cat. I have never had an indoor cat and only have experience with Blondie and her kittens - they live outside. I have a couple of questions:

1. The other cats clean themselves after they eat. How do we teach Sunny to do this? Is it a problem that she does not do this?

2. How do Sunny and Tikibird live peaceably? Can a bird and a cat live together? At times (usually when he's being loud) Sunny wants nothing to do with Tiki. Then there are times when Sunny is very interested in Tikibird.

Any help or advice that you can provide would be helpful. Thank you.

Sunny will only learn how to groom by watching other cats.
Don't be discouraged, young kittens are often terrible at it or don't do it at all until they get older.

I have a parrot and 4 inside kitties, they can peacefully co-exist, but, there will need to be some drastic modifications as far as your bird's freedom to roam.
The two should never be alone together unsupervised while the bird is out of his cage.
Cat saliva, even a small amount can kill a bird with toxic pastuerella bacteria.
The cat does not even need to bite the bird.
He can simply lick the bird, and the bird can ingest the saliva while preening.
This is why it is very important that they never be loose together unsupervised.

I can tell you from very horrible past experience that it takes less than 10 seconds for a curious cat to inflict a fatal injury on a bird without ever intending to do so.

As long as you are dilligent though, there really is no cause for concern.

The first thing I always do with new cats is to teach them that the bird cage is strictly off limits, and usually the larger birds (including feisty quakers) are great at helping to enforce this.