Does it really need no vent?

Correct. It dries by condensing moisture rather than pushing air outside, so no duct is required. You still need a drain and a water supply.

Can it be installed under a kitchen counter?

Yes. It is built as a fully integrated unit meant to sit behind a cabinet front under a counter. Check the cutout and door clearance before ordering.

How much can it dry in one cycle?

Drying capacity is lower than washing capacity, as with most combo units. Expect to dry smaller loads than you can wash, and split large laundry days.

Is the 1400 rpm spin worth it?

A faster spin leaves clothes drier going into the dry cycle, which shortens ventless drying. It also means more vibration, so a solid, level install matters.

Does it wash and dry back to back automatically?

It runs as a washer and as a dryer, and combo cycles let you wash then dry without moving clothes. Continuous wash-to-dry cycles take considerably longer than separate machines.