Regarding the weeds, and i start by saying I'm no gardener but our small lawn (20 x 30 ft) always suffered from waterlogging , poor quality soil i suspect, clay etc etc. I never had a good lawn, weeds and moss always took over, dandelions especially. One year i had it all re turfed, waste of time, i wasnt dealing with the root causes.
2 years ago i started weed and feeding it because the dandelions were infesting everything. It looked terrible for a year as they died off and left loads of bare patches but over the next year....i hardly have any weeds at all, the lawn is richer and greener than it ever has been.
Even my SIL visited and noted...oooh isnt your lawn lovely.