Learn English – the abbreviation for “state”

all-acronyms.com states that "Quest" can be used as an abbreviation for "Questionnaire".

I have seen this used before, though the word "quest" has an entirely different meaning then questionnaire does, so I generally avoid trying to abbreviate the word so that there is no confusion.

But in the context that you are using it (in a figure), perhaps if you labeled it as "quest." it would be suitable.

When in doubt, spell it out.

As for general rules, Wikipedia has the following:

If the original word begins with a capital letter, so should the abbreviation. (ex. Volume = Vol.) If the original word begins in lowercase, capitalization is not needed.

The use of periods differs between British English and American English.

• In British English, according to Hart's Rules, the general rule is that abbreviations terminate with a full stop (period), whereas contractions do not.
  Doctor (contraction) = Dr
  Professor (abbreviation) = Prof.
  The Reverend (contraction or abbreviation) = Revd or Rev.
  The Right Honourable (contraction and abbreviation) = Rt Hon.

• In American English, the period is usually added if the abbreviation might otherwise be interpreted as a word, but some American writers choose not to use one.

To form the plural of an abbreviation, a number, or a capital letter used as a noun, simply add a lowercase s to the end. (ex. Mind your Ps and Qs.)

To indicate the plural of the abbreviation of a unit of measure, the same form is used as in the singular. (ex. 1 min or 20 min.)

You're asking a question about style, as such you're more likely to find a satisfactory answer outside of the dictionary.

The Associated Press Style Manual doesn't address century specifically, but says you should "Never use an abbreviation that will not be easily understood."

Wikipedia's Manual of Style has a variety of related statements:

• "Centuries and millennia not in quotes or titles should be either spelled out (eighth century) or in Arabic numeral(s) (8th century). The same style should be used throughout any article."
• "To indicate around, approximately, or about, the unitalicised abbreviation c. is preferred over circa, ca, ca., approximately, or approx., and should be spaced (c. 1291). Do not use a question mark for this function (1291?), as this may imply to the reader an uncertainty on the part of Wikipedia editors rather than on the part of reliable historians."
• "Standard symbols for units are undotted; e.g. m for the metre (not m.), kg for the kilogram (not kg.), in for the inch (not in., the quotation mark ", or the double prime ″), and ft for foot (not ft., the apostrophe ', or the prime ′).
  • Non-standard abbreviations should be dotted."

The Association of American Colleges and Universities Style Guide discusses this issue directly: "Centuries are spelled out (CMS 9.33): the twenty-first century"

I'm sure you can find others, but to my way of thinking, your best bet is to either not abbreviate century, or use something unambiguous (such as "cent.") if you have to use an abbreviation.