Can you change the VBA background?

[Barack Obama]

Go into Memory Viewer, then in offset select "PALETTE"

At the first column of the 0500000 row, switch from 00 to 10.

Note: this will not work with Game Boy and Game Boy Color games unfortunately.

Source:
https://www.vg-resource.com/thread-31790.html

For your other question:
Different tilesets / maps use different background colours, it's the same for SNES too. Rudra for example uses black almost everywhere, but some maps have something different (green for a forest, grey for a ruined city, etc.).