Hi Jonnyng,
Glad to know that you find the application helpful. Please find below the answers to your question.
1) Currently, there is not option to share one page from the scanned PDF or to extract the page from the file to share it further.
2) It is not possible to crop the page and add it to other file using the Adobe Scan application. For that you will need the Acrobat DC desktop application.
3) By default, the files saves in the Document Cloud. There is no option to change the location to save the file. However, you can save the file on the device using the share option.
We do appreciate sharing your ideas with us about the feature you are looking for. There is always a room for the changes. You may share your suggestion for these features that you have mentioned above direclty with the team over here
Android - https://adobe.allegiancetech.com/cgi-bin/qwebcorporate.dll?YQWCX7
iOS - https://adobe.allegiancetech.com/cgi-bin/qwebcorporate.dll?XTGK8H
Hope the information helps.
Let us know if you need any help.
Regards,
Meenakshi