This is difficult to say without having any example. If you don't see all the information you expected to get for each event, I guess it was lost during the import from the FIF file.
It might be possible to read again the missing information from the STIM channels:
https://neuroimage.usc.edu/brainstorm/Tutorials/VisualSingle#Read_stimulus_triggers
https://neuroimage.usc.edu/brainstorm/Tutorials/TutMindNeuromag#Access_the_recordings
Alternatively, you can maybe find a way to export the markers to a text file from MNE-Python and then import the information in Brainstorm.
each epoch is saves as its own edf file
Avoid exporting files processed in Brainstorm to EDF.
In Brainstorm, the values are saved in the floating point double precision (64 bits), while in EDF, they must be converted back to 16bit integers. This loss of precision can cause problems.
Is there a different way to export the data that would have all the epochs in a single file that is readable by MNE or eeglab?
No solution readily available in Brainstorm, but this is something that you might able to script this yourself.
To read all the epochs in one matrix, see the last example process from this this tutorial:
https://neuroimage.usc.edu/brainstorm/Tutorials/TutUserProcess#Examples-1
You might be able to save this in the FieldTrip data format, see example from the function out_fieldtrip_data.m