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In the manual and i think in the tutorial it says that you can place all of your research slots to one tec, thus decreasing the time it takes to research something. How do you do this? Ill be researching something and have slots open but i cant get them to help research the tecs im reseraching.

It is automatic. If you have one item in research but 4 research slots the item completes faster.

It is because if we have 4 slots then we can set more money on the research, isn't it?
So actually not the # of the slots is the relevant but the money spent on researching...

Or does it make difference if I have 1 slots or 4 slots but the money spent on the research is exactly the same?

IIRC, the extra slots does increase the rate regardless of the money being spent.

I have to see that Do you have any clue about the % of the speed improvement per slot?

No, because it's not a fixed value, it is affected by all factors such as size of economy and GDP/c