1.WE say "keep one's word; go back on one's word", why can't we say "eat one's word"? In the 3 phrases ,word has the same meaning, i.e. what one had said before, I think.
2.Can we say " get a hold of somebody"?
In the second, your "words" are what you said, and you eat them because you were wrong.
When you break your word, you have shown a lack of integrity. When you have to eat your words, you are simply mistaken.
I will loan you $10 once I get paid on Friday is a promise. If I don't loan it to you, I've broken my word or gone back on my word.
You will never repay me the $10 you owe me. Then you do, so I have to eat my words.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.