1. Yes, you can receive them without worrying about your wallet and you can receive bitcoin even bitcoin is not allowed in your country just make sure that you are using VPN if you are hiding.

2. Yes, you can send them to any bitcoin addresses or any online wallets just make sure that you are using a trusted wallet like electrum to send bitcoin anonymously.

I think Bitcoin in India is not illegal according to the wiki and some news out there. So you are free to send and receive bitcoin without hesitation.