Thank you all. We bought the house last summer so I'm not sure whether the daylilies were divided (I doubt it -- nothing was done in house or garden for decades!). These are in full sun. There are some more in a semi-shady bed together with some ferns, so I might move those to a sunnier spot in fall. I'll keep my fingers crossed for flowers!

Is the area somewhat shady? Not sure, but you might compare to red fescue, Festuca rubra. hortster

Well, if you really don't have ANY time and are expecting zero maintenance, then I would suggest that the best approach is to make peace with the situation and accept the fact that some weeds are inevitable (shrug). ==>>> thats when you put 90% of your beds into wildflower meadow .. which is half weed anyway .. lol ... and then just keep a small formal garden for what time you have to do the job properly ... i have one space.. probably about 1/3 to 1/2 acre.. that i simply dont mow ... and you would be amazed at the beauty and diversity of what comes up naturally ... including all the wind borne weeds from the area farms ... and what grasses actually do.. when not shore every 72 hours .... that is also the beauty of dripping roundup around.. after dinner.. grab the bottle of scotch.. and the application.. and go spread some joy to your weeds ... its always a job.. if you have to make it a 10 hour.. all day Saturday job... but if you are just rambling around the yard.. after dinner.. as the heat cools and the sun sets.. you can kill lots of things in no time at all ... [just make sure you make it close to your own bed .. before you drain the scotch bottle.. lol .... its not good when the neighbors find you laying in the yard.. screaming obscenities at your weeds... face down in the garden bed ... threatening them with what look like a bottle of mustard ... and an empty bottle of intestinal fortitude ....] and a week later.. when they have started to shrivel ... they are real easy to pull out ... and discard.. if you dont want to let them simply compost in the garden .... man it hurts to laugh with a sinus cold ... ken

Thanks, Carol. I think you're right about the top picture being little barley. Hooray! However, the second is definitely NOT crabgrass. The seed heads are branched (dallisgrass), not helicopter (crabgrass). Here's a photo from the internet showing the difference between the two. Dallisgrass on the left, crabgrass on the right. The seed heads on my weeds look like the ones on the left. I mowed recently, but I can take more pictures of Weed#2 in a few days, if needed.