I'll see what I can answer

In what way "Diplomacy" affect the trades in "trade window"? Does it lower the cost of trade goods, or it will give me more trade options or some else?

Bingo! Basically, it increases the precieved worth of whatever goods you put forward in a diplomatic trade.

And what "different tactics" exactly gain the race with "Espionage" ability? I could only see espionage spending rate window. I don't see any "additional tactics"!

Espionage is hopelessly basic right now. Apparently it will be expanded in the future - but for now, the only possible effect of espionage trait is to increase the effectiveness of any money spent on espionage, lowering the time to increase the intelligence level for a race.

And what is the difference between "Morale" and "Loyalty"?

Morale affects your approval rating on a planet. High approval rates can give growth bonuses to your population. Loyalty affects your population's resistance to influence and your planets 'flipping' to another empire in revolt.

What is the difference between "Courage" and "Soldiering"?

Soldiering affects the strength of your troops when conducting a planetary invasion. I've never really used courage, but I believe it generates combat bonuses if your forces in combat are 'outclassed' and inferior to your opponents.

As for those first four.... I've never noticed them and can't see where they could apply. Probably related to some tentative features that never made the final game. Maybe government represents the bonus generated by advanced governments? Never bothered to check after getting one