With the ongoing development of a park outside the Government Complex at Chaeng Wattana Bangkok, the regular outdoor parking spots are now not accessible. Are there any parking spots (both indoor and outdoor) when entering from Gate 2?

Yep.

Take a right turn just prior to building B.

I parked in undercover car parking rear entry to building B.

Crowded yes but few spots available. I arrived approx 10am

There is a large parking building as mentioned above but it gets pretty busy and you'll probably end up on the top floor (in the sun) if you don't arrive early, and even that is busy.

 

There are a lot of abandoned cars there for some reason, which doesn't help.