Will Turbo tax electronically send the my NC state tax return (par year resident) to Indiana when I electronically submit my Indiana state taxes (also part year resident) or do I need to mail all the forms to Indiana?

If you elected to e-file them when you signed the return, then it'll be sent electronically. 

For confirmation of an accepted return, you should see the e-file status on the Tax Home Screen of your account. You should have also received an email from TurboTax with the acceptance status. 

How do I check my e-file status?