Is it legal to buy items, piece them together and resell them as a completely different product?

I want to be sure I'm not doing anything wrong.

Any time you create something that depends on the preexisting work of someone else, you need to tread v-e-r-y carefully. Other people's products may be protected by intellectual property laws, such as patent, copyright or trademark.

Also, what you consider a "completely different product" may not be so different in the eyes of the law. Before you start putting time and money into creating these "new" products, consult with an intellectual property attorney to make sure you're not running afoul of other people's rights.