If you have different phone numbers for different clients, can that be customized for the client reminders? For example, I use my regular number for US clients and Skype for international.

Yes, this can be done when you are creating your Appointment Types (Calendar > Appointment Types). Within the Appointment Type Wizard you can create custom Appointment Confirmations and Reminders that are specific to that appointment. 

So you would create an Appointment Type for your US Clients that includes the number to use, and another Appointment Type for your International Clients that includes the Skype information.