Just about the only thing you can do to speed up the skill switching process is to right click on the skill you'd like to change. By doing this you'll jump directly to the skill selection for that key, bypassing one page of the menus you'd normally click through.

This is the only way to speed up the process of changing skills. There is no other way to automate or hotkey skill selection in Diablo 3. It must be done through this menu.

Any 'out of the box solution' would require, at a minimum, the use of some form of third party macro or automation software, a clear violation of Diablo III's Terms of Use. While such violations are not always detectable or acted on, the possibility of action against your account and revocation of your license to play would give me extreme pause in considering any other solution.

Yes, the second Frost Nova appears to be a brand new Frost Nova, and it can cause a chain reaction if you're lucky

I noticed it yesterday when I was playing my Wizard with friends and we encountered a long line of enemies. I hit the front of the group, it Shattered and caused a 2nd Frost Nova, and that one Shattered and caused a third, and so forth.

I'm not actually sure how many Frost Novas occurred since there were a lot of enemies, but the final frozen enemy was quite a ways away from the initial Frost Nova, and was frozen around 10 seconds after I cast Frost Nova, which means at least 3-4 Frost Novas occurred.