When your knickers are in a twist, you are angry and snappish over something trivial. 'Whenever he loses his car keys, he gets his knickers in a twist.'
If someone is talking out of their hat, they're talking utter rubbish, especially if compounded with total ignorance of the subject on which they are pontificating.
('Talk through your hat' is also used.)
If someone throws their hat in the ring, they announce that they want to take part in a competition or contest.
'Toss your hat in the ring' is an alternative.
This idiom is used to describe a person who appears gentle, but is determined and inflexible underneath.
('Iron fist in a velvet glove' is the full form.)