. . . .
Anyway my questions are these:
1. How do diplomacy ships work? I sent one commercial with diplomatic module but instead of improving our relationship they demanded I leave urgently.
2. How about ELINT ships, is there a way to remain undetected, for example can i reduce thermal signature by moving slower?
3. How do I improve relationships?
4. Can I picket a moving planet at a distance?
Diplomacy ships basically give a modifier to your chances based on the diplomacy rating of the commander stationed in the diplomacy module. Any ship can get a minimal baseline amount of diplomacy if it has contact with a ship of the target faction AFAIK, and a diplomacy ship without a commander adds nothing to that over a ship without, but I believe a zero skill commander is still better than none. They wont accept a vessel in their capitol system, regardless of diplomatic intent.
Any ship, diplomatic or not, must have sensor contact with a colony or ship that they're attempting to communicate with. The contact must be visible in the system with the diplomacy ship, though it does not need to be 'seen' by the diplomacy ship itself, it could be given by a different sensor on another ship.
ELINT ships are the same as any other. Set movespeed to zero so there's a low thermal, and have good cloaking tech.
Improving relations, in terms of coding, is very exact, but in practice due to being unable to fill in the statistics for half of the equation (the targets Xenophobia, if they're in passive or active communication, or denying it entirely, their perceived 'owned' sytems, etc,) you're often left in the dark. Also, your listed relationship with them does not reflect their opinion of you. If it's neutral-low positive, they could have a low negative-neutral on you.
You could be improving your perceived score toward them massively with diplomacy, but in fact tanking their relation to you by doing it in the wrong spot.
If they suggest you leave- do so, and avoid the system immediately connected to that one with anything that is not a diplomacy ship. This is because their perceived borders extend beyond where they immediately tell you to evacuate. Even if you leave that system, don't escort your diplomat with a hundred warships on the jump point outside of it.
Yes, this will leave you with only one system in that direction to work with, unfortunately.
In general, the long story short is that if you aren't being warned to get out, and you aren't being attacked, you are slowly improving relations. Unless you're just so close that you're inside their capitol sector, then it's up in the air.
Can you picket planets? Yes. Any follow or picket order onto a planet, and before you confirm the action, change the minimum distance in the bottom left of the orders screen. I don't recall reading any changes to how that works in the C# change logs.
You can also follow their ships with your diplomatic vessels, just don't follow them where they don't want you.
Reminder, following a target means your ship is burning fuel, so you have a higher thermal and more likely to be found.
Final note, small size passive sensors, and CIWS, are both civilian components and great for high speed diplo craft if you don't want to risk as much. However, the trade off is that the size and weight, and higher needed engine power will make them either extremely slow or much more visible on thermal sensors.