The fee varies enormously according to your nationality, the number of entries required, the country you are applying in, and whether you want an express service. It is normally paid on collection, but in some localities it must be paid when you apply. A few nationalities are not charged a fee, such as Albania, Bosnia, Bulgaria, Herzegovina, Maldives, Micronesia, Pakistan and Slovakia. However, in the United Kingdom, applicants need pay more monery because ordinary passport holders should apply for from the Chinese Visa Application Service Center (CVASC) rather than at Chinese Embassy in London, UK. The CVASC charges some fees for its service provided to applicants. USA travellers have one fixed fee regardless of the other factors. The fee range is currently from about free for a very few nationalities or 200 to 900 RMB for most applicants, excluding the express service fee if you choose that.
If you have overstayed your visa and would like to remain in the country make an application, as explained above, as soon as possible and apologise for your error. If you are leaving China anyway, you can just front up at the airport or border and be dealt with there. In either case, you will probably have to pay a fine of 500 RMB per day up to a maximum of 10000 RMB though you are not necessarily denied a new application or have further action taken. However, you could be expelled from the country and prohibited re-entry for 10 years.
They operate in China and in some other countries. At the simplest they can take over your application and handle it for you, for example, China Visa Online. This is convenient if you do not live in a city where there is a Consulate, or if your situation is more complex, especially when you apply within China.
Many advertise, including in TCG, that they can be helpful that might be difficult for you to get yourself and can provide supporting documents such as invitation letters. Clearly some are more capable than others and we cannot give guidance on this except to make sure exactly what you are paying for and that the agent is genuine in being able to deliver what they promise. Many have proved they can deliver - quite simply they know the system...and usually have good contacts who can be persuaded to apply the rules more flexibly than the individual applicant can.