As the Aegis gains levels after 1st, they gain more customizations, and some for free so for example at 2nd-level he obtains evasion in astral skin form and flex skin in astral armor form. Does that mean in the morning he must choose whether his astral skin will give him nimble+speed or give him evasion, or does that mean he gets all three effects together? And his astral armor will give him brawn+improved damage or/and flexible suit?
You get all three, for each of the three cases. That means that, at 2nd level, your options are:
Astral skin with speed ×2, nimble, and evasion.
Astral armor with brawn, improved damage, and flexible suit.
Astral juggernaut with fortification, stalwart, and hardy.
On top of those free benefits, you also apply any customizations you have chosen and paid for with customization points.