This depends on how your MobileConnect long code or short code has been set up, as the details to which countries you can target is documented in the Order Form for the number.
1. Yes, to as many countries as are defined in the documentation of your MobileConnect number. If you don't have this document for some reason, you can request a copy from your Account Executive.
2. Yes. Marketing Cloud outbound interactions like SMS will consume SuperMessages, and each country can have a different SuperMessage rate. On average it's 20 SuperMessages (so, take it this way that it's 20x more expensive than an Email) up to any number, depending on the local carrier rates and how Salesforce translates these to their SuperMessages.
3. Sort of - since you will always need to have Country Code defined before you can send an SMS to some number, meaning you can always filter out the ones that don't start with a certain prefix.
Another option is to have a new Keyword for the Indian numbers and you'd be using Automation Studio to subscribe only numbers with Indian prefix to that Keyword, this way you can be sure that no international number is in the bunch.
Here are the current SMS rates in SuperMessages: