I'm new to the company but given the way things are run I would be astonished if my monitor had ever been calibrated.
When creating the artwork I used the generic CMYK profile in Indesign that I usually use. When I was ready to send it out, I converted to the ICC profile in Indesign by going to Edit/convert to profile, and I also selected that profile under output when exporting to PDF. I don't know if that was right or not, I was going on other guidance I'd found online.
I can't answer questions about why a newspaper might use certain colour profiles though I'm afraid, I don't know enough about it.
For newsprint and other uncoated papers it is important to use the correct profile because the default US Web Coated SWOP profile is designed for coated papers running on a generic web press. There would be a number of problems using SWOP for newsprint—the CMYK color appearance, which is captured by a profile, would be very different on newsprint vs. coated. And maybe more importantly, the total ink allowed would be less for newsprint. If the total combination of a color's CMYK values exceeds the total ink allowed there will be drying problems on press. The total ink for SWOP is 300%, but it would be around 220%-240% for newsprint.
Ideally you should have assigned the newsprint profile to your document when it was created, rather than working with SWOP and converting at export. Converting from one CMYK space to another can create a number of problems, most notably black text might convert to 4-colors, which would create registration issues.
Assigning the newsprint profile to the document from the start will soft proof the newsprint color limitations as you build the CMYK colors. The accuracy of the soft proof depends on both the system's monitor profile and the newsprint CMYK profile.
If you use the default SWOP you will get an unrealistic preview of what is possible on newsprint. Images should be converted directly from RGB to the newsprint profile rather than from RGB to SWOP to Newsprint. The conversion can be done in Photoshop or the images can be left as RGB and converted on export to PDF.