Please could someone explain why 'meg' is used here, and it's meaning in this context, rather than just saying "Ez lány és ez fiú"?
Well, 'meg' is like 'and the other one is', so 'Ez lány, ez meg fiú.' could be translated as 'This is a girl, and the other one is a boy.' But it's hard to translate 'meg', we use it for a lot of things. By the way, we NEVER (at least the literate part of people) use 'this' to refer to a human being, it is rude. So, try not saying 'this' to another person.
Thank you! That makes a lot of sense. Would you recommend using ő rather than ez, when referring to people then? Definitely don't want to come across as being rude!
If you use 'ő' you are always on the safe side. However, when showing a drawing or a painted picture, even the highest educated folks would use 'ez'. On the other hand, in colloquial, meant-to-be-funny conversation the use of "ő" is spreading for lifeless objects and animals as well: 'Ő a szomszéd macskája." "She is the neighbour's cat." "Melyik a legjobb boruk?" (What is your best wine?) "Ő az." (This one.)
To understand the meaning of "ez", can I say that in this sentence ez is the verb? In other word, the full order could be "ö ez lany meg ö ez fiu"?
Ez egy lány, ez meg egy fiú sounds less rude, but you can never go wrong with using ő to refer to people.
As the other people below me said, use 'ő' for people and use 'ez, az' for inanimate things :)
Why does 'meg' come after 'ez' but 'és' before?
Is it an adjective instead of a conjunction?
No, not adjective - it is still a conjuction, but a special one. 'Meg' is a so-called 'contrasting' or 'contrastive' (sorry I do not know the English term) conjuction, along with 'azonban', 'viszont' and 'pedig', which all stand AFTER what is to be contrasted, not BEFORE. In this sentence the 2nd 'ez' is to be contrasted aganst the 1st 'Ez':
Ez egy lány, ez meg egy fiú. Ez egy lány, ez pedig egy fiú. Ez egy lány, ez viszont egy fiú. Ez egy lány, ez azonban egy fiú.
See 2nd page bottom http://www.nyeomszsz.org/orszavak/pdf/ZimanyiElmeletKotoszok.pdf
since there is no 'egy' before lany or fiu, shouldn't the sentence read "This girl and this boy"?