how can a paramecium, a one-celled organism, perform all cell processes?

Answer 1

because it has various organelles that divide the functions amongst themselves, i.e there is functional specialization in the same cell for a single celled organism by division of labour amonst the specific organelle as there is division of labour in multicellular organisms by the different organs
this however does decrease the efficiency of the organism as the cell has to have a large cell volume to accomodate the different cell organelle and hence the surface to volume ratio of the organism greatly diminishes.

Answer 2

The paramecium has organelles that are specialized to perform the various processes. Since organelles are enclosed within membranes, all these processes can happen at the same time. They are compartmentalized.