Using an Arduino for a Diorama Controller
First, since you didn't mention any kind of Arduino, my answer is based on using Arduino Uno/Nano (I think its the most common)
 1. Yes you can. You use 1 transistor per building as switch (if there are many LEDs in the building) to gives optimal current and prevent your Arduino pin. The value of R2 -- Rx is depend the LED colour. You can control each group with one Arduino pin.  







simulate this circuit &ndash; Schematic created using CircuitLab


Yes you can, one in my mind is using PWM feature, like this project
Yes you can. But maybe the generated sound is not up to your expectation. Here is one of the simple example and this maybe a bit challenging.
The battery is up to your setup. More output (such as led and speaker) requires power source that can provide greater current. Arduino Uno voltage limit is 6v-20v
In my opinion, yes.


As for the form factor, I think Arduino Nano is small enough to hide in the building, while Arduino Uno size is just slightly less than a Raspberry Pi.   

Good luck for your project :)