It typically means that the lawyer’s fees are not paid unless and until that attorney is able to collect on behalf of the client.  A typical contingency fee will be anywhere from 33.3% to 40% of the recovery amount.

The value of a given case is normally measured by what probable value a judge and/or jury would assign to the case.  There is no way to know for certain what this number is.  However, in some cases a general idea as to value can be ascertained after a few hours of exploration of a given case.  On the other hand, it often may take months before an accurate value can be calculated. This is often the case in litigation where the parties must first complete some discovery against one another in order to figure out what are the strengths and weaknesses of each side, as revealed through the party’s testimony, documentation, and other evidence. In some cases value takes on a completely different meaning of value, such as “what is the value of this case to you?” but normally there are more objective measures of a case’s worth.

Yes, however it is often difficult to prove an oral contract in the absence of documentation such as an email.  It is better to have agreements in writing, and typically better to have such agreements drafted by an attorney.

Unless you are in a small claims court in California, where you must represent yourself, generally the answer is no.

A small claim in California is a case filed in Small Claims Court.  In Small Claims Court the maximum recovery that a plaintiff is entitled to is $7500 or less.  Small Claims claimants represent themselves, unless the matter is appealed, in which case an attorney may represent the appealing claimant.