Hey TIA
My definition of a gene is 'A region of DNA which may be translated into a polypeptide or a functional RNA molecule.' As for an operon, it is found in prokaryotes only, it is a 'Functioning unit of DNA containing a
cluster of genes under the control of a single promoter.' The Lac Operon contains 3 structural genes, hence I wouldn't say it is a gene itself.
Transcription factors are proteins that regulate gene expression at the transcription stage, as they regulate the expression of other genes they are regulatory genes.
The proteome is the complete set of proteins expressed in a cell at any given time, my reasoning is because my textbook says the proteome differs between cell types, not sure though.
'mRNA leaving nucleus and moving into cytosol' isn't transcription, I think transcription ends when pre-mRNA and RNAP detach from the DNA.
'mRNA binds to ribosome' I would include that in translation as it is the initial stage, but I doubt you will get asked anything like this
I'm sorry there are a lot of 'I thinks', best wait for someone else more capable of answering your questions because now I'm confused as well!