Thank you all for your replies! They are so good that I will try to give some more questions
1) If a mine gives 10 ?/year is that then of all resources or in total, ie. is it better to mine on asteroids that have many resources?
The mine rating is how much of each mineral a mine will recover each year. Mining bodies that have multiple minerals will give you more total minerals each year although which bodies will be the best to mine will depend on which minerals you are using the most.
2) Do you always need jump gates to get to other galaxies?
You can use jump drives to transit to other systems as well. Unless designed as a single ship drive, jumpdrive equipped ships will be able to bring along a number of smaller or equal size ships with them when they jump.
3) Do you need jump gates at both "ends" and if you do, will mass drivers then work sending from on system to another?
If you want two way traffic or for civilians to be able to use it then yes, otherwise a single gate will allow you to transit from the gate side to the other system but not back.
Mass drivers can't send mineral packets through a gate, you will have to send the packets to a nearby body and use freighters to transit the point.
4) In my reasoned game I played 15 years before having the Sun system invaded, is that normal?
Are you more prone to invasions if you discover other systems?
It depends on what settings you used for NPR's and spoiler races. The more NPR's the more they can explore and run the chance of finding you. They will also find new npr's that will do their own exploring triggering still more, etc. The more there are running around the larger the chance that one will find you. Similarly, the more you explore the more chance you have of finding something hostile, or if you have invaders enabled, having them show up within your explored territory.
5) In my game I played without SM but with 120000 RP (automatically set) and did not research any military techs at all, is that a mistake or should I start building up my economy first (as I tried)
I would suggest doing both rather than focusing on one side alone. If you focus only on military tech you won't have the economy or resources to support it, and if you focus only on economy you leave yourself open to hostile invaders.