You seem to fight automation quite a bit.
I don't automate my fleets, but I am surprised at your harassment. I have seen the diplomatic AI suggest doing this, is diplomacy automated? Did you approve it? I would figure the empire policy would be whether the diplomatic AI would use harassment, but I have never tested it.
5 troops per colony is a lot, depending on how many (and how rich) colonies you got. For a rich colony 5 is not a lot, but for most colony it is way more than what is sensible. It is very possible that the AI disbands troop to save money. Also, troops on ships should not be disbanded (at least not if the fleet is on manual), so if you in addition have a lot of troops in fleets it could be a high need to save some maintenance.
Fleets will act according to their posture setting. The AI messing with postures is some automation somewhere (war and attacks? Fleet formation? You seem to have automated fleet formation)
If a fleet travels a long distance to refuel, it is because there is not enough fuel closer to that. Or it is a bug :) A very large fleet require a lot of fuel at its fuel destination (enough to fill all tanks from zero to full). A gas mine will typically not have enough, even if it could cover the actual fuel need. You could manually deploy resupply ships in the areas where your fleets should operate, they will give a refuel point.
For some of your automation woes I can not comment, due to lack of automation experience with military ships and fleets. When watching the AI on fully automated, fleet management clearly shows some room for improvement.
Reputation is a modifier in diplomacy. You can see the effects there. If you have lots of trade, good past dealings, and such, it may not be very significant. Also, if you are very powerful, it is unlikely the AI will declare war on you even if they hate you. As for previous successful empires being evil, I would say they were not that successful or they would not be "previous". If previous in the same game, that is. Conquest is "evil", so any big empire is likely to struggle with reputation. The way to improve reputation is to kill pirates, and the human player may be quite good at that.
As for the suggestions: I would not put troop transports in "normal" fleets, which is where the AI puts them. They just end up killed. They are better at entering once the main battle is over. Single, automated, troop transports are good at travelling around and load troops until full, at which point they will sit idle. As long as no enemy arrive in the system they ended up in, they wait around until assigned to a fleet again.
"Don't suggest this again" could be handy indeed. I usually have diplomacy on suggest, and I get quite good at ignoring the entries on that top right list. You don't have to click them unless you plan to accept the suggestion.
The UI could be improved, but that is not for a patch of this game. Of course, something minor could happen, but no mods for UI behavior. In a successor? Anything can happen, but I would be surprised if UI will be fully mod-able.
I don't find manual fleets that bad, but I see some that use postures to keep control of the "rear parts" of the empire in later game. My games are played with no storylines and end when I feel that I have won, which is before the need for a high number of fleets arises. And if attack warnings from pirate actions are lost during the spam of war, I find it refreshing. Not being able to pay attention to every little thing at all times seems the right way to play for me.