The Nano has only 14 digital I/O pins, doesn't he? But I need 15...
No, the Nano has 20 digital I/O pins, as does the UNO. The Nano also has two analog-only pins that the UNO does not have. The Pro Mini has all these but no USB interface so you use a USB adapter to program it but when the adapter is not connected, pins 0 and 1 are freely available for general I/O use. So actually, 18 freely available digital I/O pins would seem to be quite sufficient for your needs.
~~I found this relais board and decided to use this instead of the single relays. ~~Edit: Seems not to be such a good idea.
It is indeed, a very bad design in many regards. Two of the common 8-relay boards would be quite OK.
So you mean something like the attached image ? Keeping the wires as closely as possible together such that one wire goes through the relays while the other bends before it?
That is in general, the way to do it. Note by the way, that I believe the relay common terminal is the one in the middle of each triplet.
I just saw that the relays are specified for 300V DC. Can a DC relay be used for AC?
It is quite unusual for a relay to be specified for 300 VDC. Mostly they are limited to 30 VDC due to the risk of damage due to DC arcing. These are however, reed relays where the contacts are in a vacuum and should not arc! Even so, I would be very cautious about using them to control your luminaires, especially since 230 VAC (nominally) peaks at 323 Volts. So they are not appropriate.
I think the four or 8-relay boards will be your best bet.