So for your first question the best thing is to either yes use a head band, but traditionally we have been sewing headpieces to our wigs or using an elastic headband to keep headpieces on. My Monster Hunter horns were sculpted entirely out of apoxie sculpt, and weighed in at about 2 lbs, and the elastic headband over the wig worked beautifully.
However there are situations where headpieces can be sewn directly to the wig itself, my girlfriend sews hers to her wig whenever possible.
As for the starfish carve, I don't personally thing that doing that would be a good idea. Starfish are typically very brittle when preserved in that manner and one bump and that thing is toast, and tbh I agree that it would be difficult to be identified as Misty w/o the iconic Starmie present. Personally the way I sculpt is fairly straightforward. If you feel up to the task you can use apoxie sculpt by Aves to sculpt it, however I always use some sort of wood guide to help me sculpt accurately. By that I mean I would cut out the star shape, then glue (hot glue normally) walls to achieve a uniform height on the sculpt. That doesn't make much sense, but here is a picture of a vac buck I made to illustrate it. I used wood walls to get a uniform curve for the domes.