Is is normal that my diplomats can begin negotiations with ''neutral'' or ''at war'' factions''?

My diplomats appear to be totally useless except for trading map information with those factions allied, since i cannot begin negotiations at all with any faction not allied from start. Thanks in advance.

Yep, it's normal in CoW. Diplomats are good for giving back some towns to your allies (for another town or money) if those are conquered by eg. the Chaos Undivided or the Orcs and you reconquer those and you don't need them. (I usually do this with Kislev for example if playing with Altdorf or Nuln. I send an army to the east, help Kislev, reconquer their cities and give it back to them for money).
Quests like obtain trade agreement with the Druchii as the Empire are a little problem, but you should just forget about them, as they are impractical at the moment.