Tanya, what you have written is pretty good! Well done! Some minor corrections/pointers below:

Please correct me in grammar or meaning

"To be like peas in a pod" means to be very similar with to each other.
E.g. Ann is totally like her sister, they are like peas in a pod!

"To be as different as chalk and cheese" means to be completely different.
E.g. I nicely remind you that they are, and I am, as different as chalk and cheese.

"To be the black sheep of the family" means to be the worst member of the family, it is about the person who fails in everything. (black sheep does not just mean "to fail" - the black sheep could be the one that 

brings disrepute to the family)
E.g. Billy didn't manage to enter the university… He had always been the black sheep of the family.

"It runs in the family" means something is common among members of a particular family.
E.g. Jane has a great voice as her mother and grandmother had, I think it runs it in their family.

"Like father like son" means that the father and the son are very similar with each other in something.
E.g. John can't resist the temptation to drink, as like his father before. So, like father like son.

"Blood is thicker than water" means that family ties are always more important than the ties one makes among with friends.
E.g. Blood is thicker than water and the man chose to help his family rather than his friends.

"To be given a clean bill of health" means to be called healthy by a doctor after some illness.
E.g. Today I was given a clean bill of health so nothing prevents me from attending this party!

"To be as fit as fiddle" means to be very healthy and strong.
E.g. —have you had any news of your horse this morning? — yes, he's as fit as a fiddle!

"To have a sweet tooth" means to love eating sweet foods, like candies and pastries.
E.g. I have a sweet tooth and If I don't watch it, I'll get really fat.

"To put one's finger on smth" means to identify and state the essence of something.
E.g. You have certainly put your finger on the idea of this text, great!

"To have a strong stomach" means to be able to smell, see and (or?) taste something unpleasant without feeling bad.
E.g. You must have a strong stomach if you want to become a surgeon.

"To feel something in one's bones" means to have an intuition about something.
E.g. I feel (it) in my bones (that) he will pass the exam.

"To put words into somebody's mouth" means to interpret what somebody said so that the words mean what you want and not what the speaker wanted.
E.g. Don't put these words into my mouth, I've never said anything bad about Monica.

"A piece of cake" means that something is very easy to do.
E.g. Good deeds may be a piece of cake for you but somebody can be saved by them.