What does a "non-denominational" Protestant believe? I have heard "non-denominational" Protestant churches identify themselves as such because they believe they are above the squabbling and blindness that characterizes denominational Christianity.

I have heard Christians identify themselves as "non-denominational" because they aren't really loyal to any particular denomination at the moment.

I have also heard from non- non-denominationals that "non-denominational" is in essence a denomination of itself, because churches of this identification are actually related in their origin, theology, etc. Is that true? Are there any distinct characteristics of non-denominational Protestant churches besides the name?
A Christian denomination is simply a group of churches which have agreed to work together (in over-simplified terms).  Some denominations have very rigid structures, others not so much.  They tend to share some degree of theological beliefs, but even within a denomination there may be a wide variance.

A non-denominational church, by contrast, simply does not belong to such a group.

It's quite analogous to retail chains.  Some retail chains maintain very strict control over their various retail outlets, ensuring that branding is the same everywhere, that customer service is the same everywhere, etc. Cracker Barrel comes to mind.

Some chains maintain a very loose control, allowing franchisees to set cleanliness standards, customer service standards, etc. Phillips 66 comes to mind.

Then you have one-off, mom-and-pop stores, which have no corporate or franchise oversight at all, and they do whatever they wish.  They may have the same standards of service and products as some chain stores, but not by mandate.

So asking what a non-denominational protestant believes, is a lot like asking what a non-chain store is like:  It's all over the map.

Pretty much the only thing that non-denominational protestants all believe, is that they are not Catholics.