Hi TomF-SC
iPad backups on iTunes:
1. Check what backup you have on iTunes. Open iTunes, click iTunes on the menu bar and choose Preferences. Then choose Devices from the Devices Preferences window. You shall see available Devices Backups. You may find one or more backups of your iPad.
2. Everytime you backup your iPad to iTunes, the existing backup will be updated. So, you only see one backup there. But if you want to keep one backup before doing another. Then you can right-click the backup you want, and select Archive to mark that backup untouch anymore. After doing it, you go back to the Summary tab of your iPad under Devices on the iTunes and tap on the Back Up Now to make another backup. When the process is done, you go back point 1 above and you shall see there are two backups of your iPad.
PDF files on iBooks on iPad do not show on iBooks for Mac:
1. Are you signing in with the same Apple ID on both your iPad App Store and your Mac iTunes for purchases?
If you have more than one Apple ID, the iBooks collections, bookmarks and etc will only sync when iPad and Mac are using the same Apple ID.
2. On iPad, please check Settings > iBooks, check if the Sync Collections (and Sync Bookmarks) are turned on. If not, turn them on. If already on, turn them off, soft-reset your iPad (holding Home and Sleep bottons for 10 sec.) and once back, turn them on. Then use a cable (not by WiFi) to sync your iPad and your Mac.
3. Still not working? Open your iBook, and from Preferences tap General Preferences and check the Sync: Sync bookmarks, highlights and collections across devices.
4. More steps, if necessary...
4.1 On iTunes sidebar Devices, right-click your iPad and do a Transfer Purchases.
4.2 On iBooks from File tab, select Move Books from iTunes...
Wish it helps.