Diplomacy, Trade and Alliances
The diplomacy system is undergoing improvements currently so nobody other than the devs can comment on how it will be. Right now, there are 3 alliance options: military (ships don't fire at each other), trade (trade ships go between the players), and intel (one sees what the other sees). All special abilities that target friendlies start working on your military ally (really military goes hand in hand with trade, since otherwise your trade ships would all get shot up

), which means you can combine races for some very powerful combos, and join fleets in general for massive battles.
How many ways are there to win besides war?
Currently, military is the main way to win. In FFA games, you can win if the remaining players are in an alliance (say, 6 person FFA game and 3 all ally with each other, as soon as the other 3 are eliminated, the alliance wins). Culture also plays an important role, but it's very difficult to win through culture alone if you're playing an opponent with experience.
Can you give credits, ressources and tech to an ally who is in need?
You can give credits and resources, but as the races have different techs, those aren't exchangeable.
If you form an alliance and stick together, shouldn't there be major rewards?
E.g. increased trade income with ally, ability to share repair facilities and more stuff like this?
That's how it works

Repair stations, trade ships flying to your ally's trade ports, joining fleets for attacks..
How does the 'scoreboard' work? Can you win as an alliance or does a single player win, even though he is in an alliance?
Oh, already answered above

An alliance can win, but every player in it needs to be allied with each other. For example, if player A is allied with B and C, but B and C are at war, the game won't end. But if A, B, and C are all allied with each other, the game will end in an alliance victory.
I hope this game features some kind of permanent score record. Other games already give medals and stuff like that for progressing in certain areas. I don't really care about medals, but wouldn't it be neat to see how many times someone broke an alliance and betrayed his ally? You could see at a glance who is worth trusting and who isn't!
This has been discussed and suggested, but I don't believe we ever got a concrete response on whether or not we will have a permanent scoreboard of sorts.
Game Customizations (Skirmish and Multiplayer)?
The galaxy generator has been removed from the 2 latest betas, but don't worry, it'll definitely be in at release

Will you add the feature to customize / build your own ships in a patch? In an expansion pack? Or do we have to wait for the sequel?
Do you mean design ships in game? Then no, that won't be in. It's just a different kind of game. For one, designing ships takes time, and with everything in real-time it becomes cumbersome. Then there's the whole balancing issue, etc etc. However, Sins is amazingly moddable, so you will be able to create lots of nifty stuff. There are many weapon types to play with, and you will be able to create your own meshes and such as well.
What kind of multiplayer modes are there anyway?
In truth, we don't really know

MP beta is played in Flagship mode, where everyone gets a level 3 capital of their choice for free at the start. We know normal mode will be in, where you have to research/pay for your first capital, but beyond that we don't have any info.
AI?
Because the game is still changing and focused primarily on MP balance/bug testing, the AI has taken a seat back until all the changes are finalized and a good AI can be created from the start, without having the devs re-create the AI every time something big changes. So, for now you'll hear that the AI is pretty poor, but rest assured the devs do want to give us a fun and challenging AI

Ok, one last question for now: How different are the three factions from each other - Is this game a rock-paper-scissors design?
You might hear various opinions on this. The game follows the model "easy to learn, difficult to master". The races (2 of the 3 we have access to) have similar structures, resource collection, and some similar ship roles (missile ships, light carriers, 'line' frigates), but they have diverse tech trees and special abilities. Capital ships in Sins add a lot of tactical and strategic depth to the game, and make differences between races like light and day. For example, the Vasari (experts in phase technology) have a ship that can bypass phase jump inhibitors and open a phase gate at its location to allow you to jump your fleet into that planet's gravity well from any other phase gate you have built. That means you can sneak into your opponent's backyard and jump in your whole fleet, bypassing all of his stationary defenses at the forward planets. The TEC, on the other hand, have more traditional/supportive abilities. Their carrier can instantly replenish its fighter/bomber forces, one of their support capitals can create a cease fire in the whole gravity well, so on so forth. So, while the basic way the races are played as far as construction/resource gathering are the same, there is an enormous amount of difference in how the races actually play.
And the game was specifically not designed as rock-paper-scissors, except for a select few examples (and even then, not extreme ones).