Doing a new Time Machine backup

A wired Ethernet cable connection between your Mac and the Time Capsule for the first backup will move data, on average, at about 30 GB per hour. So, it would take about 24 hours to perform the first backup.

Your current rate is significantly less than 1 GB per hour, so you are looking at about a month at the current rate for the first backup to complete.

A good wireless connection will usually take 2-3 times longer than a wired Ethernet connection, so if you elect to use wireless, the backup should take about 3 days.

The WiFi upload speed is around 80Mbps here

Something is very very wrong if that is the case. Do you mean that your Internet connection is about 80 Mbps? That would have nothing to do with the backup speed between your Mac and the Time Capsule.

Hold down the option key on your Mac while you click on the WiFi icon at the top of the screen. Scan down to find the Tx Rate. What number do you see there?

A Thunderbolt to Ethernet Adapter. is a must have item if your Mac does not have an Ethernet port.

Thunderbolt to Gigabit Ethernet Adapter - Apple

The Tx Rate is 434 Mbps. Is that upload speed or download speed?

It is the theoretical maximum speed at which your Mac can communicate with the Time Capsule. Upload and download speeds refer to an Internet connection. Backups to your Time Capsule occur over your "local" network......not over an Internet connection. So, as I said, your Internet connection speed is irrelevant as far as your backups are concerned.

If things were working correctly, the 434 Mbps connection would allow the 700 GB backup to occur in a little over 2 days over wireless.

Please post back when you have the Thunderbolt to Ethernet Adapter so we can start all over with another backup.

In the meantime, check to make sure that you do not have any kind of "anti-virus", "cleaners", "optimizers", "keepers" anything like that on your Mac, as these types of applications can and usually will drive Time Machine crazy and backups....if they work....will take forever.

If you have a wireless or wired printer on your network, that is likely the mystery item that you see there under Shared.

If your network really were being hacked, anyone who is smart enough to know how to do this will never be dumb enough to ever let his device appear on your network at all.

Once the backup is complete, power off your entire network.

Wait a minute

Power up the modem first and let it run a few minutes

Power up the next device, which might be your Time Cap;sure and let it run a minute

Power up only one Mac, the one that you use most often

Check the Shared listing in the Finder....Is the mystery item there?

Power up one more device and check again

Keep powering up devices one at a time checking as you go

Sooner or later, you will discover the mystery device.

Might be a printer, a camera, a thermostat, another network hard drive or any of number of other things.

Usually, the unknown device is the printer

All that you really need to know with an "ac" connection....or any wireless connection for that matter.....is that the more that you have line-of-sight between the wireless device and wireless router, and the closer the device is to the Time Capsule, the better the network will operate.

The other critical thing to keep in mind is if you have more than one device sending out an "ac" signal.....like another Time Capsule or AirPort Extreme.....you need to connect the routers together using a permanent, wired Ethernet cable connection.

If the signal must pass through even one normal wall in a home, the speed of the "ac" signal will drop 20-25% on average. You can imagine what things will be like if the signal must pass through several walls, or a ceiling (which is usually about the same as 3 walls as far as its density).

Very impressive speeds, if you were using wireless.