Is a lab-grown diamond a real diamond?

Yes. It is chemically and physically a diamond, just grown in a lab instead of mined. It has the same hardness and sparkle.

What do VVS1, D and excellent cut mean?

VVS1 means very, very slightly included: flaws are tiny and hard to spot under magnification. D is the top color grade, colorless. Excellent cut is the best cut grade for light return.

How does it compare with a mined diamond ring?

Same look and durability at the same grades, usually for less. The main difference is resale: mined stones keep value better, lab-grown ones do not.

Will a 1 carat round diamond look big?

A 1 carat round is about 6.5 mm across, a classic and noticeable solitaire size. It reads as a substantial ring without being oversized.

What should I know about the setting and band?

The listing gives the stone grades but not the metal, setting style or band width. Ask the seller for those details before buying.

That depends on the band metal and whether the setting allows it. Ask the seller before ordering, since a full eternity-style band often cannot be resized.