Stars: seeds from an Ornithogalum species? Is there a bulb underneath?
Methinksweed:Prickly Lettuce, or another weed that looks very simolar. White milky sap when you break a leaf?
IDK2: looks like Buddleia. Woody stem? Probably Buddleia.
I think weed: Either a Ribes species or Humulus species. Either way, likely a weed.

Thanks Dzitmoidonc - that helps - I will dig down further on the stars and see if there is a bulb and compare the IDK2 to images of buddleia (and pull the weeds, of course).

Congratulations on your new home. IMHO, you might just want to clear the yard of everything and begin anew. Build your own little paradise!
I DID!
Nursing along suspicious plants of unknown varieties is usually unfulfilling. Use your imagination and engineer your own dream yard. It isn't that hard, and done right, will bring you great happiness.

thanks budbackeast; I considered that and am not quite going that far, but I am to the point that I am going to pull anything suspicious. There are lots of tulips and roses and a big patch of artichokes that are easily identified so am keeping those and anything else that I can easily separate from being weed.

Keep in mind that "weeds" are plants you do not want growing where you do not want them. So one persons "weed" may be anothers desireable plant. One example is "Goutweed", "Bishops Weed", "Snow in the Mountain", "Aegopodium podagraria" that some consider an invasive "weed" while others consider it an attractive ground cover.
Some plants many consider "weeds", Dandelions, Plantain, etc., are grown by others as food crops. Sometimes asking 10 people whether this plant is a "weed" will often get you 15 different answers.
If you don't want that plant growing where it is growing it is a "weed" and you can get rid of it. Is a self seeded Forget Me Not growing in a crack in the sidewalk a "weed" or not?

Determining whether a plant is native vs. invasive in the sense that it is not native is objective. Many plants whether native or not are called invasive in regard to their behavior for not being a desirable plant in a garden setting. It's necessary from the context of the sentence to determine which meaning of the word "invasive" applies to that info. Is your goal to have only native plants? Or are all well-behaved plants welcome? Determining from that point what will live in your yard or not is where gardening becomes subjective.