what is name of the small screen that opens on home screen when you want to save or print a webage

On IPad, what is name of the small “screen” or “box” on right side of home screen that appears when you click the square with arrow coming out of top, when you want to save or print a webpage? Example: when I want to save the webpage or section of it to Notes or something else. I’ve searched everywhere in support, with no luck. Also, how do I move the icons around i.e. You used to be able to grab and hold the icons to move them around to easily find the ones used most often. Additionally, how do I add or delete some of the icons.

Second question: My fingerprint no longer works and I’ve cleaned the button and my finger as suggested, and reset it, using different fingers, numerous times, but it stops working after only using it a few times. This began a few months ago, along with some other quirks, like it (Bluetooth) won’t recognize/install a new portable keyboard (I contacted vendor and they assured me it is compatible with my iPad 9). Note that it’s my fourth keyboard after returning three others that I thought were defective. Would you recommend I send it to Apple since I have apple care, which expires soon. Very annoying quirks - almost making me want to bite the bullet and buy a newer iPad.

I’m 77, a little slower, please be specific when answering. Thanks very much in advance for assistance.