Can reading VGA signals from my computer harm the hardware?
Splitters are quite simple with VGA- the information only flows one way unless the monitor has an I2C identification channel. 

Damage is unlikely, and provided you follow proper procedures there is little that can go wrong. Of course if you accidentally attach any of the VGA wires to something that sends current into the output port, or there is something seriously wrong with the grounding on your oscilloscope etc. bad things could happen, as with any direct connection. 

Take normal anti-ESD precautions (touch the metal case before touching any connections or use an anti-ESD wrist strap with a high-value internal resistor to earth), make sure the oscilloscope is grounded to earth as the computer, and you should have no problems. 

Here's the pinout of a standard VGA port:  



The timing diagram looks like this: 



The RGB analog video levels should be in the range of 0 (dark) to 0.7V (full bright). Sync signals are logic level 0V/3.3 or 0V/5V.