Welcome Brekkana!
Those mounds are collectibles. Look through the collectibles screens to see which ones. Keep an eye out for a certificate being offered in the Flea Market; once you get that you can start collecting them. The certificates are expensive, though!
Only the desktop versions have the ability to change names. I know that LDW are aware that iOS and Android users would like to see that ability and I'm sure they will do their best to implement it if possible. I can't for certain answer your third question I'm afraid, although the game is automatically saved to your phone's memory anyway. I think (but am not sure) that the sharing of your achievements on Google Play is the only saving function that it has.
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