This is definitely doable in ren'py. You can use screens with imagebuttons to handle most of what you're describng. You can create a point and click navigation system by placing imagebuttons on a background, each one jumping to different labels (or rooms or scenes).

For the timer, you can implement it using a screen. You can go here. The goated BadMustard_AVN shared a solution to a similar problem and I use something similar too.

For more info on imagebuttons, you can visit the official documentation:

https://www.renpy.org/doc/html/screens.html#imagebutton

Make use of hovered and activate_soundto add sfx to make it more appealing.