The regulator is probably so the speed remains constant for as long as possible. If you connect a 12V battery to a 12V fan it will run but as the battery discharges, it's voltage will drop and the fan will lose power. Depending on the motor type used in the fan, it will either not try to rotate as fast or it will lose energy and be slowed down by the air drag. The regulator will attempt to keep a steady 12V out so the fan runs at full power until the batteries can't cope any longer. The drawback to the regulator is you lose some voltage across it, you have to put more in than you get out, that is why the two batteries are needed, to give it the extra 'overhead' it needs.
I'm not sure what you mean about the SMD LEDs, I use lots of them but they are always delivered individually or on plastic tape. I always solder to the ends, it's how the manufacturers tell you to do it. I suspect what you are looking at is someone salvaging LEDs from a 'light rope'. If I'm right, you are not seeing the normal way to use them, instead you are seeing an already manufactered device being dismantled to recover the LEDs. 'Light ropes' DO have a specified voltage so cutting them in the wrong place will result in smaller strips of LEDs with indeterminate voltage ratings. If you buy the LEDs from a component supplier you will not have this problem.
Brian.