If you want to play as peaceful Nakalim it is best to go full on exploring and expanding. Asigning relics to governors early on is not the best, you are ridding yourself 50 science and since they make barely any (no science from planets, overall system science is halved, thus a system development that is supposed to give +60 science gives only +30) it is in your best interest to leave them unassigned until you have a good stock of them. Best ways to get relics is faction questline, finding them while exploring and converting other's systems with your influence. 

As for temples on systems, it is best to fill a system with them. Five temples on one can push other empire's sphere of influence easily. (NOTE: it is better to hold off putting temples on your homesystem for a while until you have built up an economy there.) Temples only halve your planet fidsi output, which you already dont get any science from, food isnt a big deal, and you can easily stock up on dust with the religious law for +10 dust(+5 on temple planet) per nakalim pop. You also get more approval from temple planets and I am not even talking about the massive amount of influence you get.

Temples also enable you to make advanced demands to the AI you are pressuring for Economic Tribute that sometimes can basically double your science output.

Or disable awakening and save some nerves xD

So at which state do you start to convert/push other systems (aroundd which turn in a normal speed game)? i'll go for a more peacefull-economic approach neext time, and build more Lost temples. And maybe push more towards the pacifists

Is there any other strategy into cnverting/donating systems to the Academy? As said, it feels like a very late game thing. Invasions/conquest didnt seem to cut it

eXistenZ wrote:

So at which state do you start to convert/push other systems (aroundd which turn in a normal speed game)? i'll go for a more peacefull-economic approach neext time, and build more Lost temples. And maybe push more towards the pacifists

Is there any other strategy into cnverting/donating systems to the Academy? As said, it feels like a very late game thing. Invasions/conquest didnt seem to cut it

I'd start pushing other systems when you get there. It depends how far they are from you. Best way to push them is find a good 5 planet system somewhere in the middle of their empire (that isnt covered by another system's influence as they can just take it back through pacific conversion), and fill it with temples. Then wait, temple systems outperform others in terms of border growth. Slowly but surely the system's borders will take over their systems and you will be able to convert them to academy. Another way is getting to the middle of the galaxy, finding a good 5 planet system and building every influence building there, as well as nakalim counselor hero and building cathedral. Cathedral gives the system +3% fidsi bonus per temple built, which means the system itself will give itself +15%, and when you factor in all other systems that can have temples on them, it suddenly becomes ~9-12% on average per system you own, giving it an amazing boost of influence (I had one with around 14k influence production a turn) that gives a good push to your already amazing border growth. With that blob, play the waiting game until you convert other systems over to either yourself, giving you another boost of fidsi to the cathedral system, or give it to academy for 55% of the system's yields.

Invasions and military actions in general do not allow you to convert systems to academy I dont think.