You can get to lists that are created in personal space, but its not easy. Lists created in personal space are created in OneDrive rather than SharePoint. Its the same technology, but you have to use the SharePoint connector pointed at your OneDrive for Business to be able to see the list. If you use the gear menu to look at the list settings you can see the URL for the list. You can use this in Power apps in the SharePoint connector to access the list.

1) Its not visible because its in OneDrive and neither Power Apps nor SharePoint are designed to look there for lists. If you are in the List itself you can use the Integrate menu to create a Power App that uses that List.

2) Yes, all lists exported from Microsoft Lists are exported as queries, not spreadsheets. Export it as a CSV and you can open that in Excel and save it as an .xlsx
3) I don't think there is a way to migrate a List from Personal to SharePoint
4) Yes, existing lists have no option to save as a template.