after inserting my SIM card into the new iPhone, can I take it out and re-insert back to the old Android phone?

yes, phone does not change sim cards nor makes it linked to it in any way

Yes. If you have activated iMessage using the SIM then de-register iMessage

After you put the SIM on any Android follow the GIF

Watch the GIF below. Here I have used another iPhone for the demo but for you, it may your choice. Android or iPhone device.

Insert the same SIM into an Android or an iPhone. You may deregister iMessage online