Druh, if you're still struggling with 13a, then it might help to know that the first 3 letters (which are a homophone for evil, from the clue) actually read as an abbreviation of one's intention to do something, ie, it's two words, shortened with an apostrophe between the first and second letter.
Also, the 3-letter word for infant has it's final letter as the first letter of the last word. So you were on the right track with HAT.
Let us know how you are getting on!