1. Picture Viewer or do you mean Thumbnails ?
If Picture Viewer, Then no it does not auto resize when resizing size, And it is by design since it flickers to much.. But pressing Ctrl+0 will zoom image to window
2. Explorer Panel Settings, First tab at the bottom "Save on exit", Uncheck "Save only paths to local harddrive"
3. You can do that with script command and assign to hotkey. But delete file without question will not be a default action. to much risk that users messup.
4. Ctrl+F4 will sort by the 4th column. Do not think there will be a global default for it. You can do a script that opens new tab and set sorting for you.
5. The keyboard export will generate an output list for you what all your keys, It is not a backup feature..
For backup/replace use the Backup/Restore under help menu or copy the file CustomKeymappings.xml manually.