Are multi-chain proteins (especially homo/hetero-dimers) synthesized together as one overall unit or are they separate monomers which bind together at some point after synthesis, and are there any relevant factors to know about this process?
Are multi-chain proteins synthesized as one biological unit?
Sometimes yes but mostly not.
Some proteins are synthesized as one long polypeptide pre-protein which is cleaved by some proteases to yield multiple chains. After cleavage the intramolecular interactions become inter-molecular or inter-chain interactions. Insulin is a good example of this (See the figure below).
In other cases the chains are synthesized as different polypeptides which (with or without processing) subsequently associate with each other. In case of homo-multimeric proteins, the polypeptides are made by the same mRNA.
Nice answer from WYS. I would have been inclined to say that the ribosome translates one polypeptide and any associations happen post translation. Insulin is interesting in that one polypeptide is produced and then cleaved to form components of the protein so that one could say multiple parts are made at the same time if I understand this correctly. Generally the complexities of a protein are introduced after the ribosome has done its job of translation to form one string of amino acids. Protein interactions are a matter of great interest now. I'm not sure one can say any protein is formed independently but is more part of a large ochestra.