Hi!
from what I'm seeing, you have two issues here.
The first issue is that you want to bake your animation. But to bake animation onto your rig, you need to be sure, that you have all your controls or joints, whichever you want to bake the animation to, selected. Not just the groups above them, the objects themselves. Then baking the animation should work with the settings in your screenshot.
The second issue is, that you want to bake your cloth simulation. Cloth simulation is a deformation and not keyframe animation, so the edit>keys>bake command wont work for that, unless you bake on PLA (Point level animation) meaning you select all your vertices and then bake, but this is not advisable as it makes the file extremly slow and tends to crash maya pretty often. What you want to do is caching your simulation or geometry.
For this you can either use an nCache to cache your simulation itself (FX toolset>nCache>create new nCache) or cache your geometry itself, (Modeling toolset > Cache>Geometry Cache) depending on what you want to do further with your project.
May I ask why exactly you want to export it as an FBX? Depending on what program/engine you want to import in and on what you want to further do with your animation, there are probably more stable ways of exporting what you need, Alembic Caches for instance.
Tutorials:
nCache (7:39):
https://www.youtube.com/watch?v=NFa_lTm8hmM
Geometry cache:
https://www.youtube.com/watch?v=9nM6e-X_PzA
Hope this helps!