I have somehow broken the bathtub trip lever and it is detached from the inside.
How easy is it to fix it? I am worried that whatever (chain, rod) that is behind the bathtub might be falling down to the abyss. How easy is it to recover those?
Remove the two screw on the trip lever cover, and have a look inside. Since you have a plunger style, the linkage bars have likely dropped down out of view. You'll have to reach down the hole, and pull the assembly back up.
For reference, this is about what the drain looks like.
There should be a ridge at the bottom of the overflow pipe, to prevent the stopper from falling down the drain. So the stopper and linkages should be somewhere in the overflow pipe.
I've heard of people using a shop-vac to stuck the plunger out, but I've never tried it myself.