What type of grassy weed is this and how to remove it
This looks like nimblewill. It is a perennial native plant that tends to thrive in infertile soil. It has a shallow root system. Small infestations can be dug out by hand if you take care to remove the roots. For large infestations, please refer to our website for management options. https://extension.umd.edu/hgic/topics/nimblewill
Fall is the best time to fertilize a cool-season lawn and overseed bare spots. Here is more information for you.
Lawn weed management: