If you play as TEC, then there is this upgrade you can get that improves how much happiness other civs gives you, it also reduces the happiness removed when you fail a mission. Usually you want to complete the first 2 missions of giving resources, this will put them at 60+ percent. Gives you leeway to lose some points. Get a peace treaty and/or cease fire. Then make sure you explore, like 1 explorer per 6 stars, you'll need to know where your enemies are at. Then when you get a mission, do the easiest one. If they give you mission to kill 12 enemies and it is the beginning of the game, just ignore it. You'll need a sizeable fleet for that later though. Ignore the base killing, unless they are very close to you. Even if you have a sizeable fleet, you could accomplish other missions faster. But, build a fleet for that purpose of killing 6-12, it has to be fast moving, then build a second for expanding and defending. Also, missions will usually be given upon the same enemies, so building a base nearby to harrass them is good too.

Also if your playing large maps, you'll need that system to system jump technology. And make sure your fleet doesn't have to go all the way around a star to jump to the system your mission is at. That wastes alot of time, instead have your fleet on the other side of the star at a base or something, or if you can a base in the enemies home system.

It should be much easier to complete missions in 1.03; some of the times were way too short in 1.02.

OK, that's enough that you can attack 1 and have the other 2 reward you for your efforts, but it'll be close.

Generally, the idea is to pick a single front and keep attacking/attriting that enemy until they are dead and their planets are yours. Makes strategic sense, and the mission system supports it.

There is something that triggers the AI offering harrassment missions against another AI, and I think it has to do with combat-ship contact with said enemy. So, if all your combat ship vessels are on a single front, the missions are very likely to relate to that front's target, in which case simply proceeding in your overall attacks will often complete the missions. Since the needed vessels are already there, its fairly easy to switch from attacking civilian/tactical/ship targets as needed, and the sooner you finish a mission, the sooner the next mission will appear. It can add up quickly and gain you an ally from the other 2 AI. Perhaps both of them.

As to the mission times: They were fine, IMO. By making them longer, the time to 're-set' the missions is going to be too long. So if you're asked to attack a potential ally on the wrong front, it'll be ages now before that resets to a legitimate request (enemy on current front).

All this could be addressed by having a 'decline' button in diplomacy, but oh well.

One tip for actually doing the missions: The ship missions can be completed by killing any ships, including fighters and builder-drones. Fighters work particularly well, so try to keep track of where the enemy has capital ships (most have at least one wing of strikecraft). Bring your own capital or flak frigates, and in seconds you can have 5 or 10 ship kills.

I dont think you should get missions so early personally. I have found that the first two missions are generally impossible, and immediately put your AI teammates against you. Now I know you can get a cease fire and work from there and whatnot, but you should not be penalized for something that's impossible.

Also a small warning or reminder that you have a mission wouldn't hurt, I can be forgetful