A noncreature permanent that turns into a creature can attack, and its {T} abilities can be activated, only if its controller has continuously controlled that permanent since the beginning of their most recent turn. It doesn’t matter how long the permanent has been a creature.
2008-08-01 • wotc
If the first ability is activated and resolves, then the second ability is activated and resolves, Chimeric Sphere will be a 3/2 creature. It won’t have flying.