Landesschützen units were raised with the mobilisation 1939. The Mob-Plan has the number of Landesschützen units with
5292 officers, 287 officials, 22 554 NCO´s and 1149 359 men (+8700 total in eastern prussia).
The Lds.Schtz. units were part of the Ersatzheer also tactically subordinated to the Feldheer if in occuppied territories.
At the beginning of the war their duties were all rear guard and security duties .. POW´s, bridges, installations, transports etc...
Later special units like bridge-, transport guard units were formed leeaving them mainly POW guard duties. Of course some units in occupied territories were also involved in anti partisan etc.. operations.
In 1942 a Landesschützenbataillon had 3 companies (4/19/129) and a Stabskompanie. I have the KStN if you are interested.
I never saw any documents giving percentages about the fitness of members. I know that g.v.F., and g.v.H. (Garnisonsverwendungsfähig Feld und Heimat) were the two grades for the Ldschz.units.
But I agree that there is not much information to find.