Yes and no. There is no legal requirement to conduct a patentability search prior to filing a patent application. Indeed, if you are just filing a simple provisional patent application, it might be best to just file without a search. On the other hand, it is a very good idea to conduct a good patentability search before investing very much in the way of resources in R&D or patenting. If your idea is not broadly patentable, it is probably best to move on to another idea. The sooner you find that out, the better.

Probably not.  There are innumerable good search firms, both in the U.S. and in foreign countries, but they tend to search only what you tell them to search.  When you go through a patent attorney (or agent), the attorney is looking for more than just patentability.  He is also looking for modifications to the invention to circumvent the prior art, and his search will often lead into useful avenues of investigation that would never be uncovered by a patent search firm.  Many patent law firms use outside search firms to conduct their searches, but that is often because they do not want to be responsible if something is missed.

Costs range from about $500 to $1,000 and up.  Some chemical patentability searches can run $10,000.  A typical patentability search takes anywhere between one day and several weeks. Note that the simpler the invention, the harder and more expensive it is to search.

You can, and should, do an initial search yourself.  If you can find something very similar for free, you probably shouldn’t spend money having a professional conduct a better search.  However, if your search indicates patentability, you should still have a professional conduct a more thorough search.  Among other things, the professional searcher will search available foreign patents and applications which may be difficult for you to locate.

The term "prior art" is used in the patent field to mean any information that is relevant to determining patentability and scope of a claimed invention.  Prior art includes patents, journal articles, newspapers and other publications, as well as prior use, sale, and even offers for sale of embodiments of the invention.

In the United States, the scope of the prior art is determined by 35 USC § 102, which is a labyrinthine piece of writing even by government standards.  There is a thick explanation on this in Chapter 2100 of the MPEP that delineates exactly what is meant by the terms "printed publications," "on sale," "public use," "the invention," "in this country," and various other terms used in Section 102.

Perhaps.  To be patentable, inventions must be both novel and non-obvious.  Novelty addresses whether the prior art contains the very "same thing," and is the easier hurdle to overcome.  Non-obviousness addresses whether there is any teaching, suggestion, or motivation in the prior art, either in a single reference or in validly combined references, that would have led one of ordinary skill in the art to practice the claimed invention as of the filing date of the current inventor's application.  In view of the the non-obviousness requirement, it is exceedingly common for an inventor to conceive of an idea that is new, but nevertheless unpatentable.

Even if an idea is patentable, the scope of the patent will be limited to the non-obvious improvements over the prior art.

Old ideas are not patentable.   It makes no difference whether the idea was previously patented, or whether the idea was patented and the patent expired.  Nor does it make any difference whether the idea was ever embodied in a product on the market.  To the extent that an idea is old, it is not patentable.

On the other hand, inventors often devise some new twist to an old idea, and that extra little bit is what results in a successful product in the marketplace.  In those instances, the new twist can be patented.

Once a patent expires, the claimed subject matter falls into the public domain, and neither the inventor nor anyone else can recapture the lost patent rights.

This goes back to the concept that old ideas are not patentable.  If an inventor wants to extend his patent protection, he must devise a new twist to the old idea, and then try to patent that new twist.   In practice, this is very common.  Inventors and companies often hold multiple patents covering many different aspects of the subject matter.   Patent attorneys often refer to this as a "patent portfolio" or a "patent thicket."

Probably not.  The invention companies we have seen charge way too much for way too little.  The same goes for the various law office firm mills that file hundreds of applications each year.  You are much better off with a smaller firm who will really take an interest in your case.

Patent agents are licensed to practice before the patent office.  In many cases, agents are every bit as good as the typical patent attorney, and in some cases, they are far superior.

Issues do sometimes arise with respect to the purpose for which a patent agent is performing a particular task.  For example, agents can advise on the scope of a claim if such advice is used to determine whether or not to amend the claims.  However, agents cannot, by virtue of their own license, advise on the scope of a claim with respect to patent infringement.  Often the issue is moot anyway because the patent agent is working in a law firm under the auspices of a patent attorney.

The MPEP is the Manual of Patent Examining Procedure, which is a compendium of all of the patent statutes, rules and regulations.  The printed version is almost six inches thick, and covers topics from ethics to the searching, prosecution, and issuance of patents.  Copies are only about $100, and can be purchased in book form from the Superintendent of Documentsat (202) 512 - 2267.   PDF and HTML versions are available online, as well as a good searching algorithm .  The MPEP includes a terrific glossary of patent-related terms, and others are available from private sources.

Appendix L contains all U.S. patent laws.   Appendix R contains all of the rules.