It is normal for your new pup to stick to you like glue - time will help that situation, although we have found after 3 years our B still likes to at least be in the same room with us, until bedtime, when she just trots off to her bed near our bed, and curls up for the night. We cover her when we go to bed, then at some point during the night, she will jump up on the bed to burrow under the covers.
As to the cat - we already had a cat when we got our B - it took a couple of months, but it was always quite clear the cat had the upper hand if pushed, and she still does. Shiek will be fine - your pup may get a scar or two if she insists on sticking her nose too close to the cat. Now, mine pretty much ignore each other, but if it's a little cold in the house, might very well back up to each other to gather the warmth where they nap.