You cannot export Abaqus deck from Mentat, If you have access to Patran, you can create the marc model in Marc preference, and then change the preference to Abaqus, and then write out the analysis deck. Thus you can export the Abaqus input file. However all the parameters might not be supported.
From Mentat you can export the Nastran bulk data file which will have .bdf extension.
Yes. Mentat is not a generic pre post prcoesor for multiple solvers ,where as Patran supports multiple solvers such as Nastran, Marc, Abaqus, Ansys , Dytran etc...
You can import Abaqus file into Mentat, however cannot do the reverse.