It is possible to change the palette in every room, yes. However, changing the palette will affect the UI and the characters. For example, if the user interface uses palette indexes 1-12, and the character uses indexes 6-18, and you load a room that uses a palette in which indexes 1-18 are completely different, your UI and characters will look very strange.
The same is true with every Amiga game that uses the native chipset. You have to keep certain colours the same or the sprites will not use the correct colours. Other colours in the palette can change, allowing you to create different environments for each level.
Typically, you'd keep between 8 and 16 colours static (choose a few shades of red, green, blue, grey, or whatever will match your game's colour scheme - we used yellows, blues and greys, I think) - these are used in the user interface and all recurring characters and objects. The other 16 colours change depending on the environment (a nighttime hillside uses dark blues, shades of dark grey, and dark browns, whilst a spaceship interior uses a wide range of greys, light greens and light blues). Objects or characters that only ever appear in a certain room or environment can use the non-static palette indexes, as the palette will always be the same when those objects appear.
Generally, if you choose an appropriate range of colours to start with, you shouldn't need to fiddle with the palette too often anyway - just when the environment changes drastically (daytime to nighttime, planet to spaceship).
By now you should be able to see the problem with using graphics that you haven't created yourself from scratch - the palette is fantastically limited (32 colours at the most; 16 colours at worst) which is going to make intricate, raytraced or digitised images a pain to work with.
Getting the best results takes an awful lot of work, but it's possible to get some excellent images even within the constraints of GRAC if you're prepared to go back to pixel editing; the piccies below illustrate this.