How is it possible to send coins without connection?
Create the transaction offline (without a connection).
Then copy the completed transaction to something that communicates with Bitcoin peer nodes online.
This was already explained to you earlier in this thread:
Also, how do I spend/send my btc using that private key? What's the most basic way?
You create a bitcoin transaction with the appropriate inputs and outputs. Then you connect to Bitcoin peers on the internet and send that transaction to them. This is typically handled for you by wallet software. The software allows you to enter someone's bitcoin address and the amount you are sending. Then it handles the creation and broadcasting of the transaction.
Is this those smart contracts of ETH? That's what they are?
No. It's just transporting a transaction physically instead of electronically.