Your answers are a good effort however you need to work on them a little.
a) "expiry date" is the date when something e.g. a passport, some food expires.
"The expiry date on my passport is 20 June 2017".
I recommend using "expiry date" as a subject with the verb "to be" (like you did correctly in 3). It didn't work with the word "set". e.g. What is the expiry date for this food?
b) Expire (verb) "The expiry date for something" = when something expires.
e.g. The expiry date for this passport is 20 June 2017 = This passport will expire on 20 June 2017
c) Valid (adjective) This means that something can be used legally. It applies to official documents but not food. Use "valid" with the verb "to be". e.g. Is your passport valid? Yes, it will be valid until 20 June 2017 / Yes, it will be valid for another 14 months.
d) "left" (adjective) Another way to say the example sentence in c) is "Yes, there are 14 months left on my passport (before I need to apply for a new one)." It's not a very stylish way of speaking but the meaning is clear. Use this kind of phrasing: "there + some form of "to be" + [period of time] + left.
d) Validity (noun) By itself, this term is quite formal. It would be unusual to use it in ordinary life. A passport official may say: "I had to question the validity of his passport. It may not have been authorised by the right office."
You may be more likely to use the term "period of validity" e.g. The period of validity of this passport is 21 June 2006 to 20 June 2017. Again, I recommend using this term with the verb "to be".
In these situations, you will write more correct English if you use the verb "to be", as I have suggested. Try to keep it simple at first.