Heavies have a heel height of about 3.5 cm. For one thing, tap shoes have a metal plate at the front but heavies have a 'tap' of about 1.5 cm. These are quite difficult to dance in if you aren't used to them. Some heavies have tips made of wood but for some reason this doesn't seem very practical. You should aim to get heavies about half a size smaller than usual.
Heavies lace up at the front like normal shoes but also have an ankle strap for more support.
You'll need something like Vaseline intensive care or cocoa butter hand lotion. All you need to do is rub a generous amount of lotion into the shoes, making sure it has evaporated, and keep bending the shoe back and forth. Do this a good few times, and then smooth another layer on without rubbing it in properly. Also, at the risk of annoying your family, wear them as much as possible. You don't have to dance, just wear them so you get used to them and they become flexible.