1) Regarding "tertiary links" you are absolutely right. Corrected those to "roads" in this changset: https://www.openstreetmap.org/changeset/15582734

2) I agree with you about service->residential. So, I cast types of streets in the settlements around this way (https://www.openstreetmap.org/way/207894129 ) -- in this changset (https://www.openstreetmap.org/changeset/15582725). Let's see if there will be a backlash or not.
=> If there is no backlash, then can try to cast other examples you found to "residential" (I have no objections myself)

PS: "living street", by wiki is something with "A general feature of living streets is that the legislation grants pedestrians higher or equal right of way over other road users." Unfortunately, so far no one from the community ever seen a street with "legally protected" pedestrians. "Pedestrian street" sign is non-existent here. => Imo, one can safely cast all "living streets" to "service roads" without loss of information (but with a loss of misleading information)