Yes, you would wire the lamps in parallel. The current would be as you figured about 13 amps. Here in the US I would use AWG 12 wire (copper) which is about 2.05mm diameter wire. That should handle about 20 amps so it leaves a nice cushion. The only problem I see is the dimmer. You are looking at a dimmer capable of handling over 3 KW. Did you plan on building or buying the dimmer? Also, if this is an outdoor sign I would consider a GFCI line.