- Please tell me with examples, when do we use ‘tv’ without or with ‘the’?
the tv = the tv set?
tv= television ? (when?)
- Also why do we write: in North London without ‘the’: in the North London? because it is the only one area?
Thank You 
It’s a good question. I also used to wonder why we don’t use ‘the TV/television’ when referring to ‘watching TV’ while we say ‘on/over the radio’. The difference that may be observed is that ‘TV’ is always in caps. Native English users may be of more help than Google. ‘Watch TV’ has now become idiomatic, though.
As regards your second query, ‘North London’ is correct, perhaps, because it specifies a place. Here, when you use ‘the’, the phrase and the meaning will change: in/on the North of London.
However, I am of the view that we can use ‘the/a’ as in: Those professors are from the North London university of Middlesex. John studied at a North London school.
Let’s wait for other comments as well, Saneta.
Generally:
the TV - the television set itself.
“Put the book by the side of the TV.”
TV - the media of television.
“Is there anything good on TV right now?”
'Then, why not ‘Radio’? can be a question.
You can compare:
There is an important debate on the radio tonight.
Put the book by the side of the radio.
So, phrases which don’t concern a set/appliance we write: ‘‘on TV’’ and ‘‘on the radio’’.
Are they fixed phrases ? Because ‘the’ we write not before TV as the media.
It can be a question if you want it to be, but you’re unlikely to find an answer. Just because they are both forms of media don’t expect the same grammatical rules to apply.