Welcome Faithhopelove.
Some children don't focus on the ABCs and numbers and the perfectionism could be the reason why. She could very well comprehend it but until she understands the next step might not be willing to share. Also a lot of gifted kids do not learn to read through phonics and learning the sounds of letters fall under phonics. She might just know the words by sight without sounding it out and through memorization builds her vocabulary.
The major flags in your post ties to cognitive process such as the rebuilding of broken objects into something else of function for her to play with as well as the wave question. These go beyond memorization and shows advanced development for her brain. So yes she sounds gifted and I am going to take a wild guess that one day she will just have it with the reading and soar like an eagle with her reading abilities such as she did for her verbals. (again the perfectionist gene!)
