I'd suggest you read through various articles in the
War Academy section, as GP usage in general is actually very complex in terms of game mechanics. However, the short (and totally non-comprehensive) answer to your questions could be:
...The way I see it,to reach full potential of GPF i need to have Caste System civic,am I right? Unlimited artist, scientist, merchant;
Yes. That's the best way to generate a GP quickly. The downside is you can't use the whip.
And what is the best way to use may GP's? install them in my Great person farm,in my Capital,start golden ages? Thanks in advance.
Again, this is very situational. But as a general advice (excluding GGs altoghether):
1. Settling GPs in a city is usually suboptimal. There are so many better things they are capable of. The only exception being probably an SE with early Representation (Pyramids) and a super-research city or the very late game if you already burnt a few Golden Ages.
2. Golden Age: you can consider starting a GA if either you want to make multiple civic changes and are not SPI (the Golden Age saves you the anarchy), or if the

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bonus of a GA would be substantial (usually mid to late game, when you already have a huge number of citizens). It's also worth noting that a GA doubles the production of GPpts, so creating them during a GA can immediately propel you into the next one if you time it right.
3. In addition to 1 and 2 all GPs except Great Spies can bulb you technologies. A comprehensive list of GP bulb preferences can be found
here. The Great Scientist is undoubtedly the best at bulbing, not just because of the general usefulness of the techs it can bulb but also because it yields more

to the tech than any other GP (mid to late game techs won't be bulbed completely). Also, if you look at the list you will see that Great Artists and Great Priests are very unlikely to give you useful bulbs at the time when it matters.
4. All GPs have a special ability. The Great Scientist can build an Academy, yielding +50%

, a GE can build a world wonder for you (or any other building), A Great Priest can build a holy shrine if you have a holy city, Great Artists can culture bomb, Great Spies can infiltrate an AI or build the Scotland Yard, and Great Merchants can be sent on a trade mission for

. All of these can be very useful, depending on the situation and your overall strategy.
5. And finally all GPs except for Spies and Priests can found certain corporations. Again, I think there're some pretty good articles in the War Academy about them, it would take a lot more paragraphs to discuss them.
So, let's take a Great Scientist as an example, as this is usually the earliest GP you can get by building a library and running two scientists. What would I use it for?
Usually either an Academy or a bulb. They are far too valuable to be burnt on Golden Ages unless it's already in the late game and a bulb wouldn't be a huge benefit anymore.