If you are in the I/E border would that mean that you like to spend just as much time alone as you do around other people?
Also, how might one tell the difference between an introvert who gets energized by doing things alone, and one who can't get along with people and thus withdraws from them?
Even if you aren't very familiar with cognitive functions yet in the theory you'd be saying that you use your extroverted functions almost as equally as you use your introverted functions, which in my opinion is a good thing to train, though preference is still key; however, if you're as balanced as one can get on all of your function uses I would think that you would work more efficiently when problem solving.
I don't know if you have read this somewhere or not, but to Jung Introverted and Extroverted functions are always in reference to an object (whatever that may be).
As such:
Extroverts place importance on the object i.e. the object is more important to them.
Introverts place importance upon themselves i.e. they're more important.
An example Jung gives is belief in religion. He presents one man who loses his religion, but is completely fine because it was merely a tool for himself that he no longer needed. This was the introvert. While the extrovert was crushed by the lack of religion (he was excommunicated) because he'd put his entire self into that religion and he was nothing without it, making it more important.
As for your second question. I think it would be shown by the willingness to interact with people. The introvert that wants time alone, still wants to at some point join (if they aren't completely hermit like). While even after being offered to go the other would strongly reject the idea of interacting with people at any point in time. How do you see this? Well, you'd just have to ask.