Is amethyst durable enough for daily wear?

Amethyst is quartz, around 7 on the Mohs scale, so it resists scratches better than opal or pearl but less than diamond or sapphire. A prong-set 5mm stone in a dainty band is fine for regular wear if you avoid knocks and hard abrasion.

Which metal should I choose?

Sterling silver is the softest and can tarnish; 10k and 14k gold balance durability and wear; 18k gold and platinum are the most durable and the most formal. For a ring worn daily, 14k gold or platinum holds up best.

What is the center stone size and weight?

The amethyst is a round cut of about 5mm, roughly 0.5 carat, held in a prong setting with pave-set diamond accents along the band.

Is this a real engagement ring or a promise ring?

It is styled as an engagement ring but works as a promise, anniversary or birthstone ring. The amethyst center makes it a less conventional choice than a diamond solitaire.

How should I care for it?

Clean with mild soap and warm water and a soft brush, and avoid ultrasonic cleaners on amethyst. Check the prongs and pave settings periodically, and store it separately to prevent scratches.