hawkweed crazy

After 4 years of mowing for the lady homeowner upstairs from whom I rent, this year I got way more involved. I spend a lot of my own money and endless hours of my time this year trying to improve the lawn. Now I am chasing weeds around non stop and of course leaving behind the dead spots of hawkweed colonies.

Am I crazy that I think my efforts make any difference? I spend too much time by far, but I do feel some frustrated satisfaction working away. My back shoulders and hips are stiff. I have little free time for anything.

The weeds are non stop thriving in the current situation. The soil is acidic, thin mostly clay. Typically lots of moisture. I put down lime and corn gluten fertilizer early season. I have already replaced about 50sf of sod right off my patio that was far too gnarly to enjoy. I had no idea the weeds were so well established and would require so much effort.

Should I go back to mowing the weeds or be satisfied with plodding progress and keep at it? I have nomoneHere are a few pics. Will I recover any of the brown spots this year?

What kind of grass is it? Does it form a thick sod or is it just in bunches?