Desert is a land subtype with no special meaning. It doesn’t grant the land an intrinsic mana ability. Other cards may care about which lands are Deserts.

Any change to a land’s type or abilities gained by a land can affect the types of mana a land can produce.

The types of mana are white, blue, black, red, green, and colorless.

If Cactus Preserve becomes a creature but you haven’t controlled it continuously since your most recent turn began, you won’t be able to activate its mana ability or attack with it that turn.

It doesn’t matter where your commander is (or commanders are, if you have more than one because of the partner ability or similar). The value of X will be calculated using your commander’s current characteristics. (Mana value typically doesn’t change, but your commander may become a copy of something else.)

Cactus Preserve’s second ability checks the effects of all mana-producing abilities of lands you control, but it doesn’t check their costs or legality. For example, Spire of Industry says “, Pay 1 life: Add one mana of any color. Activate only if you control an artifact.” If you control Spire of Industry and Cactus Preserve, you can tap Cactus Preserve for any color of mana. It doesn’t matter whether you control an artifact, whether you can pay 1 life, or whether Spire of Industry is untapped.

Cactus Preserve doesn’t care about any restrictions or riders your lands put on the mana they produce, such as that of Bucolic Ranch or the ability granted by Discreet Retreat. It just produces one mana of the appropriate type, with no restrictions or riders.