It seems that many of the giant unicellular eukaryotic organisms (size 1mm and above) are multinucleate but there are some with a single nucleus as well (the genus of Acetabularia). My question is: do they have proportially larger organelles (mitochondria etc.)? If so, can they be seen by a person with sharp eyesight when removed from the cell?
The cell has the amount of organelles necessary to perform its function. If a cell requires a lot of protein, it must have multiple nuclei to produce this protein. If the cell performs many activities that require energy, it needs many mitochondria. So the size and quantity of the organelles will be proportional to their function, not their size. In relation to Acetabularia, it is a single-celled organism visible to the naked eye. The nucleus is visible, but other organelles are not.