I need source code or calculations that, given the day/month/year,
hour/minute and timezone (or latitude/longitude?), it can calculate
the exact lunar phase in degrees and minutes (also known as the
lunar-sun angle), and also tell youwhether it's a NEW, WAXING, etc.
moon.

Given the above lunar phase details and also possibly a different
latitude/longitude, I also need it to calculate the lunar returns for
any given period.

I'm not an expert at astrology, so explanations would be nice with the answer.

Sky & Telescope have a lot of code, previously published in their
magazine articles.  Have a look at
http://skyandtelescope.com/resources/software/article_326_1.asp

If you can get hold of a copy, Jan Meeus' "Astronomical Algorithms"
has a huge amount of information.

Ian G.