Wrong on almost every point.
The actual facts are:
Karl Marx (your statements are about as accurate for Groucho Marx) and Engels both co-wrote 'Das Kapital' (one of the rare theories that is substantially less accurate than its predecessors - because they confused how they thought the world should be with how it is) and the Communist Manifest - https://www.marxists.org/archive/mar.../Manifesto.pdf
The latter is obviously highly relevant for this thread. The actual manifesto part is
That is a political action program - written by Marx and Engels as members of the communist party, and clearly on the left.A spectre is haunting Europe – the spectre of communism.
...
They (Communists) openly declare that their ends can be attained only by the forcible overthrow of all existing social conditions. Let the ruling classes tremble at a Communistic revolution. The proletarians have nothing to lose but their chains. They have a world to win. Working Men of All Countries, Unite!