When native Chinese person sees new, unknown character - how one learns it? :
-knows pronunciation and meaning by basing it on/from radicals
-has to check pronunciation and meaning(if yes - where? in dictionary?) and memorize it to use later?
From what I've seen, radicals are not taught in China. Children learn characters from a dictionary and then memorize them. It's pretty much the same system we use, learning the most common characters first.
Young children's books in China are pinyin with the characters above the pinyin.
All students in China use XinHua dictionaries. Look at the pictures below for Chinese learning tools used in China.
Children are writing characters everyday in China, so memorizing them is not really an issue. Although, just a we can forget how to spell English words sometimes, of course Chinese children may forget how to write a character. It's the same.
In Taiwan they do teach radicals more, but in either case Chinese speakers don't do a lot with that stuff. However, they also know lots of characters, so they can easily relate a novel character to the thousands they already know well.