What does “I’ll give you undercover!” mean here?

Question

I have no idea on the meaning of “give you undercover” in the following citation.

“ ’S’ up, Figgy?” he said, staring from Mrs. Figg to Harry and Dudley. “What ‘appened to staying undercover?” “I’ll give you undercover!” cried Mrs. Figg. “Dementers, you useless, skiving sneak thief!” (Harry Potter 5 [US Version]: p.22-23)

N.B.: He and Mrs. Figg were supposed to guard Harry without Harry’s knowledge, but while he was absent from the duty, dementers (evil ghosts) attacked Harry, when Mrs. Figg’s identity was exposed. This scene is just after he came back. (Dudley is a boy accidentally involved in the attack.)

Here are my questions. I’d be glad if you could help me.

1. What’s the undercover’s part of speech?
2. Is there any reason she’s using the same word as he?
3. What’s the meaning of the whole sentence?

Answer 1

I'll give you [something] is a sarcastic and furious reply when [something] is initially said, in this case, "undercover".

Here, Mundungus Fletcher is saying that Mrs. Figg is supposed to be an undercover agent and isn't supposed to reveal herself. However, the appearance of the dementors completely destroys the purpose of remaining undercover since their presence would have revealed the existence of magic to innocent bystanders, if there were any. Fletcher is ignorant of these events, despite the fact that he was supposed to be guarding Harry, so Mrs. Figg is angry that Fletcher wasn't there.

Essentially, the basic meaning of the general construction is

No, you're a complete idiot; the whole premise of your statement is based on facts that you were supposed to know but didn't or were misinformed about.

An alternate meaning in certain circumstances is

I will deliberately misinterpret your statement because I am angry with you. (Certain examples on TVTropes)