I am a beginer in polish language and i want to know if expression ja cię dobrze znam
is grammarly correct to explain to someone that I know him/her well.
What is the context? What do you, specifically, want to express?
As it was already mentioned, this particular expression, albeit grammatically correct, sounds pejorative - like in "I know you well and I know that you're up to / you did something evil". If the context is neutral to positive, I'd rather say "znam cię dobrze" or "dobrze cię znam" - but still, I can hardly imagine using this kind of message in an entirely isolated statement. To me it always sounds like an introduction to criticize or to praise someone.
What is the correct noun instead of cię to express the plural of respect to someone
who is elder for example?
You have to decide what do you want to express.
In modern Polish plural (second person, to be precise) is NOT used in a honorific sense. Second person plural is just plural, ie. it is used to address a group of people in a non-honorific way.
Second person plural used to be used in a honorific way indeed, but it was in the 19th century. In the 20th century - at least in the second half - mainly by the communist party members or state / military / police etc. officials, probably under the influence of the Russian language.
In other situations third person singular was (and is) used, similarly to the Spanish or Italian, except that typically "Pan / Pani" is used as a personal pronoun, instead of "usted / Lei", depending on the gender of the addressee. Similarly, third person plural, with the pronoun "Panowie / Panie / Państwo" (masculine, feminine, mixed) is used to address a group of people in a honorific way.
However detailed context would be needed as well because specific ways of addressing people - within the said third grammatical person structure - vary depending on whether you want to address a stranger, a known person who deserves special honorification (elder, superior) or simply is not close enough, an elder family member (grandpa, aunt/uncle, parents), intended level of formality, etc.