Is it possible to backup my files onto the Time Capsule by doing so through the Ethernet Cable, and then continue the rest via wireless backup, or will it always have to be done by using the ethernet connection once a backup was done using an ethernet cable.
If you want to disconnect the Ethernet cable from your Mac to the Time Capsule and log on to the wireless network with your Mac, backups will occur over wireless.
In general, you should expect wireless to take 4-5 times longer than the Ethernet connection, so if you have a large backup as a result adding a lot of new photos, movies, etc,, you might want to re-connect the Ethernet cable and turn off the wireless on your Mac for that backup.
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I believe wireless backups and wired backups are incompatible, but is this not the case when comparing a wirless backup to that of a backup done via USB.
No. Backups made over a network can be done via Ethernet or WIFI. In fact, we (and Apple) recommend the first, full backup (and any large ones, or full or large restores) be done via Ethernet, as it's so much faster.
The incompatibility is with network backups vs. those made "locally" (to a directly-connected USB or FireWire disk). Those are stored differently from network backups. See the blue box in #E2 of Time Machine - Troubleshooting for details.