Single field instead of several fields
"Are there any advantages to remove all this tables and use the
  following Users table instead"


It depends.  Are you talking about a lot of rows?  Or just a few?  How about the number of different data fields in a "People" document?  Parsing something like that (for a lot of fields) is not going to be easy or performance-friendly.  Especially if the fields are not consistent across the documents.


  "Where people are document with a special structure, for 
  example, JSON or XML?  This database is not truely relational"


Given these statements (and others) it almost sounds to me like this particular instance would be better served with a (NoSQL) MongoDB solution.  Essentially, you could have a "People" database and save collections of "Parents", "Friends" and "Colleagues."  MongoDB stores documents in collections as BSON, or a binary-encoded serialization of JSON.

Here's a link to the MongoDB site which explains a little about BSON and MongoDB.  Hope this helps.