It's rather physical closeness. If you want to express personal/social closeness, you would rather say: "Jestem Ci/Tobie bliski" (I am close to you) or better "Jesteśmy sobie bliscy" (We are close to each other).
In the last one you mean 'We are close to each other'. I'm close to myself by definition ;)
I think it can, but as noted in the previous comments, usually there's a better way to express it.
'Next to you' was marked as wrong.. English is my second language, so just to check: is the difference just that 'next to' is closer than 'close'?
Maybe it's this... or maybe it's how it doesn't allow for the more metaphorical interpretation discussed earlier... anyway, it just somehow seems wrong to me as a translation of 'blisko'.
They are both used for singular 'you', they are both used for Accusative and Genitive.
"cię" is the neutral form, the basic one. "ciebie" is emphatic.
so "Lubię cię" is a normal sentence meaning "I like you". You could say "Lubię ciebie", but it sounds like "I like you (but not him)".
The emphatic form is a must at the beginning of the sentence (granted, such sentences aren't common). So "Ciebie lubię" is like "You - I like". I can imagine a dialogue "-You don't like anyone! - I like you." and "Ciebie lubię" could work there. But as I said, it's not common.
The most important thing is that prepositions need the emphatic form (for pronouns that have such a distinction, of course). so "Jestem blisko cię" wouldn't just be unnatural, it would simply be wrong.
Actually some pronouns have a special n- form that is used only after a preposition and it's a must then. For example let's take Genitive masculine: "Nienawidzę go" (I hate him), "Kocham ją, a jego nienawidzę" (I love her, and/but him - I hate), "Idę do niego" (I am going to him). All instances of 'him' are in Genitive and they have different forms.
Following on from RhonaSergi's question, I too would like to know why 'I am near to you' is not accepted as a translation of the above?
It seems it isn't a construction known to any of the course creators, nor to me - it wasn't until moderating this course that I learned it can be correct and started adding it where requested. Added here.