Frequency-to-Voltage convertor diagram questions
1- The diagram you used was drawn in a simulation software. You need to specify a ground reference node in most simulation softwares, that means that you need to tell the software which node has zero potential or voltage. the triangle you see at the bottom of the diagram shows that the node it is connected to has zero potential. It is not a transistor or any other component. .tran 10 as Felthry said in the comments is a way of telling the software to perform simulation for 10 seconds. you don't need to worry about that niether.

2- Basically when the sonsors output is greater than 12.7 volts the diode and transistor conduct and output voltage gradually goes up to 12v. when the sensors output is lower than that the transistor turns off and the capacitor in the output starts discharging gradually to zero. I guess the gradual rate of the changing output plays an important role in this application. This rate is determined by the values of the resistor and the capacitor in the output. I'm not sure what you are asking but I hope this answer helps you understand what happens in the circuit and figure it out by yourself.

3- I believe you got that, its 12v.