Warning: Time Machine is not an Archiving application. It keeps rolling back ups. That means if you delete something from the source Mac it will eventually be also deleted from Time Machine. How long that takes depends on the amount of disk space TM has. So, remember, backing up in Time Machine is not the same as Archiving.
For the blank thumbnails: This can happen if you try delete too many photos at one go. Experienced users suggest you should delete in batches of 100 or so.
Yes you can split the Library, where some of the Masters are stored locally and some on an external disk, but really, you don't want to do that. iPhoto's file management tools are limited at best, and if the path to the files changes then you could find yourself repairing the links to the files - all of them, one by one.
Better: Have your entire Library on an External Drive.
Make sure the drive is formatted Mac OS Extended (Journaled)
1. Quit iPhoto
2. Copy the iPhoto Library from your Pictures Folder to the External Disk.
3. Hold down the option (or alt) key while launching iPhoto. From the resulting menu select 'Choose Library' and navigate to the new location. From that point on this will be the default location of your library.
4. Test the library and when you're sure all is well, trash the one on your internal HD to free up space.
If you want to have a smaller library on your internal disk:
Here's one way to do what you want:
Make sure the drive is formatted Mac OS Extended (Journaled)
1. Quit iPhoto
2. Copy the iPhoto Library from your Pictures Folder to the External Disk.
Now you have two full versions of the Library.
3. On the Internal library, trash the Events you don't want there
Now you have a full copy of the Library on the External and a smaller subset on the Internal
Some Notes:
As a general rule: when deleting photos do them in batches of about 100 at a time. iPhoto can baulk at trashing large numbers at one go.
You can choose which Library to open: Hold down the option (or alt) key key and launch iPhoto. From the resulting menu select 'Choose Library'
You can keep the Library on the external updated with new imports using iPhoto Library Manager
Regards
TD