Dear Aamir,
Answering your first question, this is excerpt from Microsoft Troubleshooting and this is applicable to all versions just not 2015.
"Be aware that Internet-facing deployment (IFD) is required if you’re using Microsoft Dynamics CRM 2015 (on-premises version). The system administrator must configure claims-based authentication before users can access Microsoft Dynamics
CRM data with CRM for tablets. If you have your Microsoft Dynamics CRM website available over the Internet but it is not using the Microsoft Dynamics CRM IFD configuration,
it is not supported."
So yes, its necessary to configure IFD. Refer the link
https://technet.microsoft.com/en-us/library/dn660982.aspx
And coming on to your next question I must say that I may not be an expert here but is the CRM URL registered in the Internet's root DNS servers, If not i dont think it will never work for a client on the Internet. Domain names on the Internet
have to be registered and the IPs used by it and its sub-domains must be configured and available via a publicly accessible DNS server.
Hope it helps!
Regards, Abhishek Bakshi If you find this post helpful then please Vote as Helpful and Mark As Answer. Check my blog on https://mydynamicscrmblog.wordpress.com/