If they start shooting, then they don't like you.

Nah I don't think that's right Steve

When Can I propose them commercial/alliance treaties? and how? The other jump point to WISE got a red jump gate, what does that mean? I know for sure that they are exploring WISE and the next system, what should I do? What are your advices to stay in peace (for the moment)?

Best way to keep improving relations (from both ends, since you can see how your empire feels towards them, but not the other way around - you could have 108 diplomacy rating with them but they might hate your guts) is to avoid systems they clearly tell you not to visit and to allow trade access whenever the option is available.   The diplomatic ship should also be used constantly, it nets good diplomatic rating from both sides - the fact they also use one suggests they aren't inherently hostile towards you.   Eventually it should be possible for them to send their civilian freighters to ship goods to and from your planets and viceversa - that would also improve their diplomatic rating towards you.   Having such a close neighbor is always dangerous though, even if they look friendly.   In your situation I'd design some jump point monitors - either ships or platforms you could move around with a tug - and park them on the jump point.   Just in case! Lost a very interesting game due to me having 200+ diplomacy rating with them and them not really reciprocating the sentiment and sending 20 missile ships to send Earth back to the stone age.  Also, the red jump gate (aka stabilized jump point) just means it was one of their ships that stabilized it and not one of yours.

I've got the same scenario: Their home system, their suggest leave system next to it, my colonised, suggest leave system next to that.  So far parking my diplomatic ship in their suggest leave system is gaining plenty of diplomatic rating and they seem content to tolerate it sitting there indefinitely.

A diplo ship that is 10kt or less should give no penalty to relations because 10kt is subtracted from diplomacy ships in the calculations, afaik.  So I assume this is how we are supposed to do it.

I've got the same scenario: Their home system, their suggest leave system next to it, my colonised, suggest leave system next to that. So far parking my diplomatic ship in their suggest leave system is gaining plenty of diplomatic rating and they seem content to tolerate it sitting there indefinitely.

An option to give diplomatic ships access to your systems but not military ships would be a good improvement. We are getting along well enough now I am tempted to remove the suggest leave status on my neighbouring system, but I am worried they will colonise bodies in that system, and others, that I plan to use eventually.

FWIW, the diplomatic rating increase that shows in the event log comes from THEIR diplomatic ship talking to you. THat's why you are getting that even without a diplomatic ship on site.

Thanks for that info, I think that was one of the main things I was misunderstanding. Does that mean if my diplomatic ship increases my diplomatic rating with them, but there isn't a diplomatic ship of theirs in the area, that I can get increases with them but won't have it reported in the event log? This is where I seem to be having trouble increasing diplomatic rating with the two other NPRs.

Can confirm passives count as detection, just found my 5th(?!) NPR, I am only ten years in and started the game with 1 NPR. These guys were detected by my new commercial engined Geosurvey class, which just has passives. Without a diplomatic ship I am already getting a diplomatic ratng increase on my events log. Do you think the previous two NPRs could be some kind of spoiler race or something, or just have very hight xenophobie? I just don't understand why I can't open diplomatic channels with them, yet they are not hostile.

Sometimes communication simply isn't possible, after a period of attempting to communicate with little positive progress your diplomats will eventually just give up and you'll see a message in the event log along the lines of "Diplomats attempting to translate the language of <Alien Race> have abandoned their efforts. They insist they are just too alien to understand".

I have never come across a non-hostile spoiler, and if they're sending territory demands then they're most definitely not traditional spoilers as those don't communicate in any way, they just exist in their system and engage anything they pick up on sensors.

Do you think the previous two NPRs could be some kind of spoiler race or something, or just have very hight xenophobie? I just don't understand why I can't open diplomatic channels with them, yet they are not hostile.

yes, probably spoilers

Active size 1
EM size 1
TH size 1

are all commercial.

I think NPR go with signature reading from the engines to determine if a ship is either commercial or military, however when they detect active sensors they assume the ship has some sort of offensive capability or at least this is what I understood observing tgeir behaviour.

Maybe you notice more activity as when you activate the activevsensor your ship becomes visible from much further away therefore activating detection but as suggested already you can just activate your transponder to ensure you are seen and then engage the NPR in a close range to ensure lock.

Regarding detection itself I think an EM or TH signal should count as detection as long as it's both ways, but now I am not sure...