I also spent a lot of time manually removing some of the
weeds, but that doesn't seems to help as the very next day
my lawn is yellow again from dandelions
I have missed.

Dandelions must be removed by the entire root, since they will sprout
from roots remaining in the ground. Use a good tool like the Ergonica
Weed Twister to make sure the entire root is removed.

Frankly, from looking at your photos, you should probably start with
some major changes as suggested above, in order to get to the point
where individual weeds can be attacked with the proper tools.

Ray
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Talk about weeds: World of Weeds www.ergonica.com