What do you mean, view sky through projector? Do you mean you have a camera outside, and you want to project the video from the camera with the projector? It depends what your video source is.
The cables also depend on what your source(s) have for output
The PS2 may have composite, S-Video and component outputs - check your unit
You do not need a TV
The projector will display whatever source you give it with the appropriate video connectors and resolution
Here are the specifications for the projector
https://www.manualslib.com/manual/237793/Epson-Emp-62.html
it is 800 x 600 Dots (SVGA) resolution
It has an analog VGA input (D-Sub connector)
And it has Composite and SVideo and component video inputs for analog input
It does not take a digital video signal (DVI, HDMI, DisplayPort)
It has a stereo minijack for audio output (like a phone or iPod) so you can send stereo audio to your speaker set
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