is it possible to send and receive texts while on airplane mode using internet only?
Yes, so long as you have a WiFi connection. You may be limited to SMS texts, but it depends on the WiFi provider. Otherwise, RCS and other forms of modern, encrypted texting are always using data so are going through the internet anyway.
I don't think so. When airplane mode is activated, it turns off/pauses cellular data, WiFi and Bluetooth. I could be wrong but I'm pretty sure this is not possible.
You can turn back on WiFi with most newer devices after activating airplane mode. This is how airlines supply in-flight WiFi. The same thing was also being done when I took a cruise last year. Everyone had their phones in airplane mode, but if you bought the internet package from the cruise line, it was running through the ship's WiFi.
