Does the Viking VDOE527 need a special circuit?

Yes. It runs on 240V and is hardwired, so it needs a dedicated 240V circuit installed by an electrician. Confirm the breaker size against the installation guide before ordering.

What is the difference between the two ovens?

Both cavities are electric ovens, so you can bake in one and roast in the other at the same time. Check the manual for which cavity handles broiling and self-clean.

Yes. It has a self-cleaning cycle that burns off food residue at high heat. You still wipe out the ash afterward.

Will it fit a 27-inch cutout?

It is a 27-inch-wide built-in double oven, so it is made for a 27-inch cabinet cutout. Measure the cutout height and depth as well, since double ovens are deeper than single ones.

Does it have convection?

The listed features cover self-cleaning and a timer, with no convection mode named. Treat it as a conventional bake and broil oven unless the spec sheet for your unit says otherwise.

How does it compare with a 30-inch double oven?

A 30-inch double oven gives wider racks and usually more features, but it won't fit a 27-inch cutout. The Viking's advantage is fitting that narrower space with two ovens.