Yes. You could have put commas after Howard and Center, but they are not strictly necessary.
Short answer : Yes and not impolite at all, as suggested below. This is to be handled by you grammatically correct? requires inverted commas to be correct. It should be written as: "Is this sentence "This is to be handled by you." grammatically correct?" The sentence is correct but not very polite; it would be simpler to say "You are to handle this"
Yes, because "from the Cancer Research Center" is an appositive, and it must be set off by commas. Jane Howard, from the Cancer Research Center, gave me your contact information and suggested I get in touch with you. Appositives refer back to the subject and give more information about the subject: Amelia Earhart, the famous woman aviator, died mysteriously in 1937. There are also some people who would suggest another comma, after "information"-- gave me your contact information, and suggested I get in touch with you.
This sentence is not grammatically correct. For the sentence to be grammatically correct, the space between "in" and "to" would have to be removed. Therefore the sentence should read "They are into skating."
"That was wrong" is a grammatically correct sentence.
The sentence is grammatically correct.
Yes, the sentence is grammatically correct.
Yes, the sentence "his hand is filthy" is grammatically correct.
Yes. Strictly speaking For example at the beginning of a sentence is what is called an "absolute," grammatically unconnected to the rest of the sentence.
Yes, it is grammatically correct.
'Rhoda's crazy' is grammatically correct.
'What a drunkard you are' is a grammatically correct English sentence.
No it should be "You were not there"...