It's hard to tell for sure without seeing the context that the expression is used in, but there is a slang usage for "all that" that Ms. All That could be referring to. A lot of times when someone says "she thinks she's all that," they mean someone who has a heightened sense of self-importance. It's sometimes meant to mean someone who is egotistical and thinks the world revolves around her. "She's always wears expensive clothes and brags about everything. She really thinks she's Ms. All That." Depending on how it's used, however, it could also be used in a positive way. "Wow! She donates to charity and also volunteers at the animal shelter? She really is Ms. All That!" "All that" can be used as a slang term to also mean cool, or someone who has their life all together. Like "Beyonce is so cool! She's really all that!" Sometimes we say things like "Mr. or Ms. Know it All" when we are talking about someone who thinks they know everything. Similarly, "Ms. All That" could mean someone who thinks they are the center of the world or the most important. (Or when used positively, someone who can do a lot of things or does a lot to help people.) So depending on how it's used, it could be taken positively or negatively. You can use the speaker's tone of voice (if it's spoken) and context clues to figure it out.

No idea. It should be given in the article where you saw it.

Here Ms refers to a title a woman has when she does not want to be known as Miss or Mrs. The author is ridiculing the title of Ms.

Perhaps just a lady whose pet phrase is "all that"? Or the speaker uses this nickname to show the kind of impression the lady has left him. You know what "all that" means, right? Might be sarcasm, like sometimes, "oh, is it that good?"