improving my relations with others

Military action is the most important aspect of relations. You won't like players who blow up your stuff and vice versa. Likewise if you blow up their enemies' stuff, your relations will increase. If your opponent is attacking you or even just sitting there, it may impossible to get a cease fire. Once they do some damage to an enemy of yours, your relations might rise to the point that you can get a trade agreement, which can slowly increase relationship in proportion to your trade between each other and is a good building step to a cease fire.

Another thing worth mentioning is that as xenophobic, genocidal maniacs the TEC Rebels are probably the least diplomatic faction in the game. I'm not sure how they think of the TEC Loyalists of the top of my head, but everyone else can forget even trying to work with them. The Advent and Vasari Rebels might be better candidates for diplomacy, as you three are implied to have an alliance in the trailer at the beginning of the game.

Yeah..

I had the same question.

To improve YOUR opinion of other fraction try giving them missions, ask for money and envoys after you research such options. In effect your fraction's opinion of others improves the same way their opinion of you does

I usually start with money, crystal requests - depending on the race - TEC are keen on credits for instance.

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Actually there is an exploit - if you playing against AI - can give them any resource as a present and immediately ask for the same amount back - you get your resources AND improve their opinion of you.

 Yeah I read the tooltip and started offering missions hehe. Never thought of asking for money/resources though. Gonna try that. You can ask them to send envoys? I don't see an option in the missions section to do that or a tech which would enable that.

you can change type of the missions in the mission screen, as well as fraction and the level.

If you have preferred AI fraction - research main diplomacy technologies, bribe them, start trading -> cease fire -> send envoys immediately to all their planets, ask them to do the same, go for the easiest level of the mission.

When both of you have discent amount of envoys - 8-10 in total - it is a matter of time to reach scoring of 10 and above.

If it is 3 AI map - you can do the same with another AI of your choice - but chose wisely, because the remaining AI wont be willing to raise negative score with bribing for ceasefire. Perhaps you can try purely diplomacy orientated strategy right from the start, before getting penalised by other fractions for not completing their missions. So you could theoretically be able to build relations with all your AIs. 

However, there is a drawback - I do not know how to make your opnonet to offer you pacts.

Is it a matter of supply and demand, so is you have good relations with a couple of AI, they just start to compete either you have to sit tight for them to research pact since those are not their priority...

The big hold back is usually the AI being slow to research them, and there's not a whole lot you can do about that short of giving them enough money to ensure they have a maxed out fleet. They'll start researching more when they can no longer build ships.