I believe that they would get their primary and secondary structures forming naturally from the sequence of their amino acids, which is a result of the sequence of nucleotides in the mRNA strand, the secondary by Hydrogen bonding between closeby R groups and that the 3D functional shape would be from proteins in the cytosol that are specifically responsible for folding proteins into particular shapes, akin to what chaperone proteins do?
And this would be the same mechanism in prokaryotes?
Secondary sticture results from hydrogen bonding between the regular repeating amino acid backbone and not the variable side chains. hydrogen bonds that form between side chains fall under the tertiary structure classification.
Protein chaperones do not determine the folding, but simply facilitate and help it along. The folding of the polypeptide is still determined by the sequence of amino acids and the properties of the variable side chains of that sequence.
This would be more or less the same in prokaryotes
This question is quite similar to the previous one.
How might prokaryotes modify their proteins and have functional diversity in their proteome?
The primary and secondary structures I understand, but how do proteins in prokaryotes get their 3D functional shape if there is no rough er to do this for them? How are proteins in prokaryotes modified, like how do they make speciliased proteins, such as RNA plymerase and carrier proteins?
Thanks. 
the rough ER does not give the protein its 3D shape, it rather contains proteins which can modify the protein by such mechanisms as cleavage or the addition of carbohydrate chains.
Here it is the case that protein cleavage (for example) can occur in the ER, but also in other places (like at the ribosome). As such, it can occur for proteins in prokaryotes and for proteins which aren't being secreted by eukaryotic cells.
This is just from a brief read, so It may be incorrect in some ways.
You can read more about it here:
https://www.ncbi.nlm.nih.gov/books/NBK9843/ Let it be known that a lot of this is all beyond the knowledge of VCE biology; all you need to know is that protein folding occurs determined by the sequence of amino acids and protein modification occurs. With protein modification like cleavage you only need to know it in terms of secreted proteins in the endomembrane system (i believe), and you do not need to know the precise enzymes or what not, just that the polypeptide chain is cleaved as part of producing the proteins functional 3d shape.