That all depends on :
a) length of cable
b) make-up of cable (number of strands of what cross section per core) or better still the resistance of the cable/metre
c) current drawn by the load
3.5mm are OK for low currents 10s rather than 100s of mA. You might be able to push an amp or so through them but you could end up with contact problems = heat = even more contact problems. Lots of gadget chargers use 3.5mm plugs as charge leads so they are capable of carrying current.
Have you thought about using RCA phono plugs/sockets. These are much bulkier but they can carry a lot higher current than the 3.5mm jack.
The 2.5m long strip will draw 1 A.
I will ideally need 4 meters of cable between he power source and the light.
Should I pick the classic electric cable used for any kind of lamp? (which has a 2x 0,75mm section.) or can I go for a thinner section?
The thinner is the better in my case (I need this cable to have a really soft sheath.)