Q:

Are both 遠く and 遠くに adverbs?  If yes, are them interchangeable? 

The i-adjective 遠{とお}い means far, distant.  From what I know, I can make an adverb out of an i-adjective by replacing い with く, which should give me 遠く.
Now, the word 遠く is also a noun itself, which is interesting.  This is nicely explained in this question. 
Now, in the song Yume Sekai (ユメセカイ), by Haruka Tomatsu, we have:

遠くに聞こえた鐘の音が少し寂しくて 
[...]

It looks like 遠くに is working as an adverb here.  Is this correct?  If this is the case, then can both 遠く and 遠くに be used as adverbs, with the same meaning? 

A:

No, 遠く is a noun meaning "distant place".  The sentence means "The sound of a bell heard in the distance was a little melancholy".  
Compare:
遠くにある建物    A building in the distance
遠くから見える灯台      A lighthouse visible from afar
どこか遠くへ行きたい   I want to go somewhere far away

