Your question was a good one and I am glad it was asked because I have wondered the same thing. Thanks for the good answers.

301A can do it but the top fabric tends to 'flag' around the needle unless you have project in a hoop. this works for small design, would not free motion quilt this way..IMHO...just to likely to cause injury....which would interferr with fun (aka sewing) time. have never tried it with the BERNINA 1630 because she has every foot made (such a Diva). :)

I have a Bernina 1230 and have only done FMQ with a hopping foot (darning foot) on it. I have used it both with feed dogs down and feed dogs up. Feed dogs up gives better control with some quilt sandwiches. Feed dogs up may not work with a non-spring FMQ type foot. It really depends on your machine. Some machines FMQ easier with feed dogs up.

I have removed the foot upon occasion when I've wanted to sew really close to a bulky item such as a buckle that wouldn't fit under a presser foot.

The foot goes up and down with the movement of the needle. It does touch and hold down the fabric while the needle is in the fabric. It just doesn't in conjunction with the feed dogs, hence you are the feed dogs and you move the fabric. Hope this helps.

I am unsure what type of machine you have but my FMQ foot is adjustable. i can turn a screw on the top of it that will allow the foot part to go closer to the layers of fabric. I have a Janome Horizon and 6600