1. grand central station has constellations painted on its ceiling, so the text is talking about the ceiling
2. take a chance on means that he would be basing his decision to have a relationship with (or meet in person) this woman based on her appearance. when you take a chance on something you decide to do something even though the outcome is not guaranteed to be what you want. it's similar to saying "bet on".
3. by the way this woman is speaking it sounds like she comes from the southern or midwestern united states, where this type of expression might be more commonly used than, say, the northeast.