Using noodle cooking water to loosen sauce?
I always reserve a bit of pasta water to add it to the pan. The reason is simple: if you drain your pasta and add it to the sauce the pasta will suck up all the sauce and become a bit dry. Adding the pasta water ensures that your pasta will remain moist. Also yes, it helps thickening the sauce (this does not necessarily apply to tomato sauce).

Now, let's be clear: you DO NOT add your pasta water to the sauce when you are preparing the sauce. You only add it when you put your pasta in the sauce. It also helps if you don't drain the pasta, just take it out of the boiling water (using tongs, ofc) and put it in your sauce while still on the stove. A quick 30-50 secs stir and that's it.

Hope this helps.

PS: 1/2 cup seems like a lot to me. For two portions of pasta I usually add around 3 tablespoons.