Can I clone my existing MacOS and Windows partitions onto a new SSD in my Macbook Pro?
Yes, you can use CCC to clone your OSX partition, but not the Windows/Bootcamp. (source: CCC Help). If you read that carefully, it says that it can clone the win partition, but won't make it work afterwards.

To clone and make your windows partition bootable, you need to rely on a Windows utility. Take a look at this thread (or google "clone my bootcamp partition") for a good starting point.

Booting from the SSD will be a matter of putting the SSD in the machine and turn it on, if it's the only drive, it will boot from there.