You need a DC-DC adaptor. This is a 12V car battery to laptop adaptor. They should cost around £30 or cheaper. Most are around 60W, get a more powerful one depending on the laptops power requirement, 70W > perhaps?
The SDC, yeah just solder the wire to the power button. Some solder them to the docking station. If your laptop support wake on ring through the comport then you can use this. Some can only wake up from standby but not from fully off.
No need for tank because the laptop already have this.