pathfinder 1e – Does Improved armor and armor stacks?

No, these bonuses do not stack.

The Astral Armor entry says

When formed into astral armor, an astral suit resembles masterwork chainmail and is treated as such for all mechanical purposes. Should the aegis be wearing armor when forming his astral suit in this fashion, the astral suit encloses the armor and the aegis gains the benefits of only his astral suit and not that from his armor, even if his armor would confer better benefits. Forming an astral suit into this form takes a move action. The aegis gains the following free customizations: brawn, improved damage. At 2nd level, the aegis gains the flexible suit customization as a free customization when the astral suit is in astral armor form. At 8th level, the astral suit resembles and is treated as a masterwork breastplate for all mechanical purposes.

And the Improved Armor ability states:

The astral suit thickens and strengthens, increasing the aegis’s Armor bonus by +1. This customization can be taken once for every five levels the aegis possesses and stacks with any Armor bonus granted from the astral suit itself. The aegis must be at least 5th level before selecting this customization.

Improved Armor specifies that it only increases the bonus that the suit provides, and the Astral Armor ability specifies that it doesn’t stack with any armor you are wearing.