[Nick White] "BUT I AM ALWAYS TOLD THAT PROJECT SETTINGS ARE CRUCIAL. WHY? WHY?/WHY? "
Because the project properties affect the video preview, and the video preview is what you are using to make all of your editing decisions. If you're making editing decisions based on inaccurate data, your render is likely to not resemble what you expected.
From reading your posts I can see that you've already seen that not getting your Aspect Ratio correct will indeed affect your render. All of your cropping an positioning decisions are made based on the aspect. If you get that wrong, things wont be cropped or positioned correctly in your render (if the render uses a different aspect).
I believe you also mentioned that getting the Deinterlace Method correct is also a critical setting. This is correct. If you don't tell Vegas how to deal with interlaced footage, you will get a mess when you render.
So it's not that the project properties directly affect the render, but it will affect how you edit, which will in turn, affect your rendered output.
[Nick White] "WHY do I match it to the source?"
This makes sure that you are making edit decisions based on the true resolution and aspect ratio of your footage. If your project properties don't match your footage, Vegas will convert your footage into the project properties before showing it to you in the preview so you will be editing based on the project properties and not your footage properties (but this may be desirable sometimes as seen in the next answer)
[Nick White] "What happens if I have various sources....frame sizes/rates? "
Then you have to decide what you want to use to make your edit decisions. In this case, I usually set the project properties to match my delivery format. If I have multiple delivery formats, I set it to make the highest resolution format. The real key is that you have it match the delivery aspect ratio so that there are no surprises when you render.
[Nick White] "But do the _Project settings have any effect on the rendered video_? "
Not directly. The project properties affect how you see your footage while editing and indirectly affect the rendered video if you were making edit decisions in one aspect and then render in another. Also the Deinterlace Method is crucial if you are using interlaced footage so that Vegas knows how you want to handle the interlacing.
Does that help?
~jr
http://www.johnrofrano.com
http://www.vasst.com 
