In terms of Jewish astrological signs and influences on people, per Kabbalah, would a ger use their actual 'birth' date or their date of conversion which is considered a rebirth?
first I would like to make a comment about your use of the word astrology. G-d's blessing to the Jewish people includes within it the idea that the Jeiwsh peopleare above being influenced by astrology and that instead our helpand success comes directly from G-d.
There are two seperateideas in regards to a converts age. For all practical implications a conver is the age they are however the day in which the conversion happens is like a birth in the sense that a new aspect of the serson has been revealed that was not before the conversion happened (similar to an actual birth when a child within the mother is revealed to the world) in this sense the convert is like a newborn. Many who say tehillim after shachris say their tehillim which they know based on their age plus one will say the psalm corresponding to the new aspect of their spiritual identity.
in terms of marriage, putting on tefillin, etc you are the age by which you are known to be physically.