I believe that the 1st Marine Division fought against the Russians, while the 2nd Division fought against the Western Allies. A book, "No Grand Procession" covers the clash between the British and Canadian forces and the 2nd Marine Division. Actual combat appears to have been limited to April 1945 through the end of the war. The Allied attempt to build a bridge across the Kuesten Kanal, and the German success in blowing it up twice, is one of the key engagements.
The Marine Infanterie in this area had training very similar to normal German infantry training, and wore similar uniforms. A few (Wehrmacht ?) combat veterans were scattered in the units to provide the benefit of their experience to soldiers from a branch of the military that had no experienced ground troops to draw on. Weapons included the usual K98 Mauser, MG42 machine guns, Panzerfausts, and some captured enemy weapons such as Hotchkiss machine guns. In combat the tent-half (which was camouflage cloth) was commonly worn over the uniform. The "Russian Pear" style of foxhole was used, with a small hole opened wider at the bottom, and if possible a board with grass clumps covering the small end for camouflage. Tactics included the "silent machine gun nest", which let itself be bypassed by the enemy, and opened fire when the main defensive line opened fire.
The Allies were surprised by the sudden appearance of motivated and tough troops, after having dealt with a number of hastily assembled and unmotivated units over the previous weeks.
The Marine units were severely outgunned and outnumbered, and were either surrounded in pockets or pushed back steadily by the Allies.
Apparently the purpose for their use in the West rather than against the Russians was to hold back the Allies as long as possible, so that the maximum number of German refugees could cross the Elbe river, and thus escape the Russians.