Looks like the speed signal might be 5V pulses: There is a pin for sending 5V to the speed sensor and another for receiving "signal" (written in Chinese) from the speed sensor. The RPM signal looks to be similar: 5V pulses.
Some of the lights will just need a transistor to switch to Ground. You can tell which ones by connecting the pin to ground to see if the light lights up.
Other lights seem to require a 12V input. That will be trickier. If you can find some tiny relays that will switch 12V DC and have a 5V 30 mA coil you could use those.
The fuel gage and water temperature take a variable resistor, possibly to Ground. Transistors, like used for some of the lights, on PWM (analogWrite()) pins might be sufficient to control them.