First
It looks like it's possible to set custom validation rules, but I'm wondering if there is any way to customize the validation messages (I need them to be in Arabic).
Second
Is it possible to reverse the direction of paper-input floating label (place it at top right instead of top left).
First
paper-input exposes a error attribute you can use to declaratively set a custom message. If you want to use core-input directly, that element exposes a setCustomValidity(message) for setting it.
http://www.polymer-project.org/docs/elements/core-elements.html#core-input
Second
That would be a good feature request to file against paper-input. I was able to get something working using CSS overriding, but the internals of the API could change in the future.