The word “category” is superfluous.
No, it’s not. Without it WP would “percieve” the URL as for a Page.
And you can replace the word with anything that fits better your blog.
Yes, it is. At least WP is smart enough to know that if I don’t have a Page named [category], it shows the category content.
Try it out, tcob.com/category/tech and tcob.com/tech are identical.
I think it’s reasonable to expect (the option of) category links generated in the shorter format. I’m sure it’s also easy enough for me to write a function that would do it for me, but I’d just like to know if a standard method already exists.