The grade applied to a book is a combined result of many factors, mainly reliant on condition. You can find more details here.

Common defects include:

Edge wear on the dustjacket
Soiled pages
Torn or missing pages and/or dustjacket
Fading
Writing on the pages or cover (unless by author)
Damaged corners

Basically, general wear and tear on the book.

If your book originally came with a dustjacket, then yes, that will hurt the value. However, there are many other factors, so don't just assume it's worthless, get it appraised!

An appraisal is always good to have done, regardless of whether you plan to keep your collectible book forever or whether you plan to sell.  An appraisal increases the provenance and value of a collectible book and increases the sales potential of your book. Insurance companies will often not replace collectibles without a third party appraisal, making an appraisal a necessity. Your collectibles should be appraised once a year, so that you always have the latest value of your collection should the unfortunate happen.  Appraisals also give you the power of knowledge.  Many times people have sold a book for a few dollars when that very same book was worth thousands of dollars.  If you take your book to a bookstore and ask the bookstore owner to work for free and ask that owner what they believe your book is worth, do you believe they are going to tell you the whole truth?  You should not expect a person to work for free and you should not expect a person who stands to make thousands of dollars from your lack of knowledge, to give you the entire story.  That is why collectors need an independent appraisal of the value of your collectible books.

Warmly inscribed and inscribed are used interchangeably meaning that the signer has addressed his autograph to a particular person, ie 'To Billy Bob."

FlatSigned means the autograph is directly on the book, not on a bookplate or sticker, then stuck onto the page of a book and is not personalized such as "To Billy Bob."  

A FlatSigned book is generally considered more valuable than an inscribed book and is more desirable to many who collect rare books.  There are exceptions.  If you have a full page of writing from Ernest Hemingway or John Steinbeck as examples, those full page dedications would be considered more valuable than an autograph alone.  The other exception is if the author has personalized the book to a person of note or relative.  Books signed on bookplates are almost never more valuable than those which are FlatSigned.

It depends. Is the autograph by the author? If so, yes.

To know whether your collectible books are as they were described when you made your purchase.

To increase your knowledge of your collectible books.

To increase the value of your collectible books.

To have a written report of condition (which affects value greatly) in case you need one for your insurance company in the event of a loss.

To share with your friends and family this added value and information of interest corresponding to your collectible books.

To know the value of your collectible books in case you wish to sell your collectible books.

To be able to better compare your collectible books with others on the market.

A book becomes rare when there are few of them available on the open market.  A book becomes valuable when collectors desire a particular book and the demand for that particular book exceeds the quantity available.  A rare book is not always valuable.  If no person wants a book, then even if there is only one in the entire world, that one book is worth nothing.  The more demand goes up and in correlation to the scarcity of that title, the more the value will increase.

The term First Edition is sometimes used interchangeably with the term First Printing but technically, this is not correct.  A First Printing of a book is a book printed during the initial print-run, when that particular book was first released to the general public.  An edition of that same book may include many printings but generally, the only books which are rare and collectible are those books which are both First Editions AND First Printings.  A First Printing "Thus" is a first printing of a later edition.  This occurs when a new publisher releases a previously released title or even when the same publisher releases an Anniversary Edition.  First printings of these later releases may also be valuable.  Be sure you know what you have before selling or discarding those books you have available to you.

No. As a general rule, modern books do either state their printing or give a clue to their print by a string of numbers on the copyright page. Distinguishing a specific printing can be a daunting task, hence our existence.  Some publishers do not state printings on the copyright page and often, bookclub editions are very similar to the real thing.  Each publisher follows their own rules in designating what the first printing is and these same publishers often change their own rules or make mistakes and re-print what may appear to be a first printing but is not.   Although there are many books printed on the subject of identifying first printings, the only way to know for certain is to consult a professional.

No, this depends largely on the specific book or type of book being examined.  Most signed/limited/numbered editions have no jacket but may come with an original slipcase or acetate cover.  Many other books are produced without dustjackets or any type of cover.  The only way to know which ones are which would be to investigate directly with the publisher, rely upon books written on the subject which themselves become outdated or proven wrong, or to consult a professional with Book Grading Service.