IIRC the EP/Biolakis typikon says that Alleluias are done on Saturdays that have no major saint or major feast and the days of the Great Fast, so according to it you'd sing God is the Lord during Advent.
Advent is a special fast different from the others. It is less stringent and liturgically it does not have changes related to the fast. There is no prohibition of liturgy during the week and in some cases liturgy is served everyday. We do not switch to the anaphora of St. Basil. Let us also not forget that the fasting requirement are much less during most of the fast. It is only after the feast of St. Ignatius that we go into our normal strict fast.
We have talked about advent before, usually around this time every year. If you wish to talk about other aspects of Advent please look at some of the other topics. Here is one I found on the fasting practices... http://www.orthodoxchristianity.net/forum/index.php/topic,18530.0.html
Another interesting discussion on western vs eastern in regards to Advent/Nativity Fasthttp://www.orthodoxchristianity.net/forum/index.php/topic,4558.0.html
More on liturgical practices, in particular Sarantaliturgohttp://www.orthodoxchristianity.net/forum/index.php/topic,13850.0.html
These are just a few of the topics people may want to look at or comment on. I am sure there are a multitude of other threads in other sections of the board.