These idioms describe how someone handles a conversation, and all three are informal — natural in everyday speech and casual writing, but too colourful for a formal report. To beat around the bush is to avoid saying what you really mean, so pointing it out is a mild criticism. To hit the nail on the head is to say exactly the right thing, so it works as a compliment. To break the ice is to say or do something that makes people relax at the start of a meeting or conversation. Each is a fixed phrase, so you cannot swap the words.
Getting to the point
beat around the bush /bit əˈraʊnd ðə bʊʃ/ — Stop beating around the bush and tell me whether the project failed.
hit the nail on the head /hɪt ðə neɪl ɑn ðə hɛd/ — You hit the nail on the head; the real problem was the deadline all along.
break the ice /breɪk ðə aɪs/ — She told a quick joke to break the ice before the interview began.
Not ""Stop beating around the tree." (the word is fixed; it is not 'tree')" — say ""Stop beating around the bush." (the fixed idiom for avoiding a direct answer)". Idioms are fixed units. The phrase is always beat around the bush; changing 'bush' to 'tree' breaks it and means nothing in English.
Try it: Which sentence uses the idiom correctly to mean 'you said exactly the right thing'? (You hit the nail on the head about the budget being too tight. / You hit the nail on the top about the budget being too tight. / You broke the ice about the budget being too tight.) Answer: You hit the nail on the head about the budget being too tight. — 'Hit the nail on the head' means to identify something exactly right, which fits here. 'Hit the nail on the top' is not a real idiom; the fixed word is 'head'. 'Break the ice' means to make people relax at the start of a conversation, not to be correct.
Nerves and high prices
These idioms are all informal, everyday expressions, and their exact form matters. To get cold feet is to suddenly feel too nervous to go through with something you had planned. If something costs an arm and a leg, it is extremely expensive — usually said as a complaint. A blessing in disguise is something that seems bad at first but later turns out to be good. Note the plural feet and the fixed word order in each phrase.
get cold feet /ɡɛt koʊld fit/ — He got cold feet the night before the wedding and almost called it off.
cost an arm and a leg /kɑst ən ɑrm ənd ə lɛɡ/ — The repairs cost an arm and a leg, so we sold the car instead.
a blessing in disguise /ə ˈblɛsɪŋ ɪn dɪsˈɡaɪz/ — Missing that flight was a blessing in disguise; the later one was half empty.
Not ""He got cold foot and cancelled." (singular 'foot' is wrong)" — say ""He got cold feet and cancelled." (the fixed plural form)". The idiom is always cold feet, plural. 'Cold foot' is not English; you cannot make an idiom singular just because it feels grammatical.
Try it: Which sentence is correct? (The tickets cost an arm and a leg, so we stayed home. / The tickets cost a leg and an arm, so we stayed home. / The tickets cost an arm and a hand, so we stayed home.) Answer: The tickets cost an arm and a leg, so we stayed home. — The idiom has a fixed form and order: 'an arm and a leg'. 'A leg and an arm' reverses the words, and idioms cannot be reordered. 'An arm and a hand' swaps 'leg' for 'hand', which breaks the expression; the words are set.
Try it: Your friend was furious when her train was cancelled and she had to stay overnight, but that is where she met her business partner. Which idiom fits? (the cancellation was a blessing in disguise / the cancellation broke the ice / the cancellation cost an arm and a leg) Answer: the cancellation was a blessing in disguise — 'A blessing in disguise' names something that looked bad at the time and turned out well, which is exactly the cancellation she was furious about. 'Break the ice' is about relaxing people at the start of an interaction, and 'cost an arm and a leg' is about high price, neither fits.