The first objection does not even address the issue. A large supply of low skilled workers simply means a large supply of unemployed individuals if there is a minimum wage put in place. So we can have a large supply of “extraordinary low” (extraordinary compared to what?) wage earners or a large supply of unemployed individuals. Which is better? I would prefer to have a bunch of low wage earners contributing to a productive process than a bunch of unemployed individuals. Finally, giving someone a job (at any wage) is not exploitative so long as the employer is not using force.
With regard to the second objection, welfare has its own arguments aside from the minimum wage. There are moral and economic objections against welfare. When discussing welfare, I like to ask the proponent of welfare if it is permissible for me to break into their home and steal their food if I am hungry. Further, the expropriation necessary to fund welfare (whether through taxation, debt or money creation), is destructive of wealth.