1. Do I need to purchase a domain name with the same name as of my Internal Domain?
You need to buy a domain with -MX
2. Do I need to purchase Webspace as well?
3. I am not sure how to use and configure MX Records? Do we need to create an MX Record at our end or on the ISP end?
4. Do I need to purchase a plan for emails as well?
It depends on what this really means. if the provider is providing POP/SMTP then you don’t need to configure these internally
If you are planning on having users send and recieve emails from yahoo or hotmail accounts, you don’t need anything more than Outlook or a similar Email client. You can configure Outlook to synchronize with external email accounts very easily. Just remember sites like yahoo and hotmail will require that your users purchase a subscription to allow them to use Outlook. Gmail currently does not require a subscription.
You can use YPOPs for Yahoo, it is free.