1) I'm afraid not. You can simply bookmark the URL with the sort by whatever field you like and use that as your home page.
2) Are you using user accounts? If so, most settings (the non device specific ones like margins/font sizes/stylesheets/etc) should be automatically synced between devices.
3) There is space on larger screens, not on smaller screens, and there are already way too many items at the top level.
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