Title mostly says it all,

About the other question I was wondering, will we be able to morph into different colored parrots other than just one?

Mostly fixed Parrots in 1.0.3 (CF, GH). They're still a bit wonky due to... something, but it's better than nothing.

Regarding mob variants, it is something I would like to explore, but I need to think of a good way to do it first. I could provide extra options at the bottom of the morph screen for setting mob-specific data (eg. rainbow Parrot, or whatever).