Have Last Updated on Records Auto-Update and Fixup Manga DB Method

More prep for managing items deleted through the website/other clients.

These changes now set things up so the "lastUpdate" value is updated
every time the record is synced from the website. The next step will be
to detect records that were not updated, thus deleted from the website,
and purge them from our database.

Additionally, updated getMangaRecordsFromDB to function more like
getAnimeRecordsFromDB so it will be more readable.

This brings us some progress on #19.
Add clearDeletedItems Method

Add the new clearDeletedItems method and call it after we do a list
download/sync. This closes issue #19.
Rename lastUpdate in the List Sync

Use the name currentTime for the lastUpdate variable as it better
describes the value.