I provided a source. It's literally published by the municipality. It doesn't get much more official than this. You can also get the exact shapes at https://data.gov.lv/dati/lv/dataset/apkaimes . The names are also in LĢIA name database and they are classified as "pilsētas daļa".

Yes, I made a couple typos when transcribing because there were a lot to add and I didn't notice. The solution is to fix these or let me know and I will fix them.

There is no available center point data, so I placed them approximately around the shape's centroid. Which ones were misplaced? Again, let me know and I'll fix them. Or feel free to import the boundaries, I have not had the time to do that yet.

Which other names are wrong and/or illogical? You fixed only two which were obviously typos and not otherwise wrong. Everything else seems to match the dataset's names and the names given in the article. 

I am not sure how being a local matters, but if you can provide a source from the municipality which acknowledges that these are not considered valid names or divisions by the municipality, we can go further with this.

But it is completely inappropriate for you to delete this data. Please revert your edit and fix or point out any errors so we can fix them.

As far as verifiability is concerned, I have provided 3 official sources, but you only claim they are wrong. https://wiki.openstreetmap.org/wiki/Verifiability