You do not need third party software to partition a new drive (though you certainly can use a 3rd party app if you prefer). Simply do it through Disk Management.
You do not "transfer" the images to the external drive. When you create the image you create it on the external drive. The imaging software app will allow you to save the image to any connected medium you choose (cd, dvd, internal drive, external drive, etc).
Macrium Reflect is probably your best choice as a free app.
Size of the drive is up to you, as is the brand. Just stick with a name you know (ie, WD, Seagate, etc).
As for updating the backup, I use Acronis True Image so I'm not sure of Macrium's options. But with True Image you have the choice of creating a full backup or an incremental backup. The latter will append changes to the original image. I prefer to just create a new image weekly and I always keep the two or three most current images (just in case one of them is corrupted). When you create images be sure to use the "verify" option. It will take longer, but it confirms the image is both accurate and good.
Never heard of a reverse backup. Stop listening to idiots.