Wow, a lot of questions.

You contrasted "really reading" with sight reading, which is what I did at first, but I've since given up on the distinction. A lot of people sight read almost exclusively, even as very literate adults, and they are certainly "really reading." Other people read almost exclusively phonetically. The way your DD learns to read will be a mixture of sight words and phonetic guesses--the sight words will become more numerous and the guesses will get more accurate as she gets more practice.

Personally, I like the distinction of "learning to read," "reading," and "reading fluently." Your DD is in the learning to read camp at this point. When your DD starts reading new books (books she's never been read) to herself for pleasure you can say that she's reading. And when she starts reading everything in sight with understanding and without hesitation--when it is rare that she needs help with a word rather than rare that she reads a word--you can say that she's reading fluently. Typically that final step happens at about the 3rd grade level (or, at least, it did for DD).

Yes, kids begin by being able to read some words and gradually progress to reading more and more words, until they can read just about anything. For most kids, the process is pretty slow, but for gifties it is often very fast. DD progressed about one grade level every two months just after her 3rd birthday until she was at about a 4th grade level. Then she slowed down, probably mostly because books that are above that level aren't interesting for her, for the most part. You can check out reading levels for books you have by looking them up in the Scholastic Book Wizard. But keep in mind that as with everything else, gifted kids are often asynchronous in their reading development--they may have comprehension far in advance of their decoding skills, or vice versa.

Should you pay attention? I am hugely in that not paying attention camp with gratified3. Perhaps it is my personality, or DD's, but in our case any interference at all would have been a huge mistake. DD taught herself in her own way, and she did an amazing job.