Can I recieve messages from someone not in my contacts? Am I able to recieve or send text messages from a android user if I don't save their number and my airdrop is turned on to "contacts only"?
AirDrop and text messages have nothing to do with each other.

AirDrop lets you use your iOS device to send or receive files from nearby users who also have iOS devices.

Text messages are just that - text messages. You use the Messages app to send or receive text messages to or from any cell phone number.