Hey there, welcome. The terms product design and industrial design are interchanged quite a bit in the states. In Europe there seems to be a slightly stronger differentiation. In the case of Stanford, which is probably the school with a product design title on your list, it tends to be more theory based.
The categories of product that you have interest in are very wide spread. Those are the things that most of us are interested in, but a school that has specializations in automotive design may not be one that has a great furniture program… not to mention that the skill sets taught are very different and taking all of that on in 4-5 years would be daunting. Automotive design in particular is a ver specialized sub set of designer with high skill set demands and, as you might expect, a lot of global competition for relatively few positions. Automotive design isn’t just about a profession, it is practically a devotion… For automotive, you best bets in the US are likely Art Center, CCS, and The University of Cincinnati.
I’de recommend The University of Cincinnati as a very good all round school.
For furniture, and more hands on softgoods type work, I would look at RISD.