I understand it's frustrating trying to use a language you don't understand. And instead of reading the language manual you go on rambling.
"" is an empty string (almost) as you know it from other languages.
character(0) is an empty vector of type character (i.e. a vector with no elements). This vector doesn't even contain an empty string.
R is a vectorized language. You almost always deal with vectors. "" actually is a character(1), a character vector of length 1. Once you understand this, there is a chance for you to enjoy R.