The first two are definitely a weed, though I don't know its name. I have done the same as you, let that plant grow into the large sprawling thing you have there in hopes that it was some sort of volunteer beauty, but no, it's not. It has flowers, but they are insignificant, and the plant, while not as unattractive as some, is just not anything you want in your flower bed. The good news is that it is not a particularly noxious weed. At least around here (Southern CA) it doesn't reproduce that wildly. Just pull it out. The third photo looks like some kind of wild geranium; that is, a true geranium, not a pelargonium. At least around here, those are quite nice to have.

Not a doubt in my mind with the supporting photographic evidence that it is knotweed. I would have come to the exact same conclusion just based on your description - the rapid spring growth; the hollow, bamboo-like stems and even the coloring are all classic attributes of this pernicious weed.

Euphorbia of some type ? does have some really nice nice cresting developing It's a pretty happy camper right now do yourself a favor and don't check for what color is inside. I would avoid any type of poking , pot moving. pot turning or any thing that would only tick it off at this time.

Anthony, I would like you to reconsider using any weed and feed products. They have some rather serious drawbacks: 1) they are not very efficient at weed control and you are using an estimated 30-60% more herbicide (the "weed" portion) than necessary because of the broadcast application method distributing the herbicide where it is not needed. 2) W&F products are a major contributor to water pollution. Because they are applied so frequently and so heavily where not specifically needed and because they are water soluble by nature, they leach into groundwater and are carried off into our streams, rivers and lakes. They contaminate drinking water, produce algae blooms and can damage or destroy aquatic life. The most common contaminates of our drinking water and of our lakes and streams and other waterways are the chemicals typically found in most W&F - atrazine, dicamba and 2,4-D. 3) Because of their size and metabolism, children are more readily affected by pesticides than adults and W&F products contain ingredients that can be extremely harmful to kids. And pets! They can be endocrine disruptors and produce negative effects on the immune system and there have been links established to non-Hodkins lymphoma. The herbicidal granules are easily tracked into the home on shoes, bare feet, clothes and toys and pet feet and pads. in a 2003 study, 2,4-D was found in abnormal levels in 63% of homes tested for air quality. If you feel you MUST use some sort of herbicide to control lawn weeds, then pick a dedicated spray product that you can apply directly to individual plants. Because these are liquid sprays and not granules, they do not leach into groundwater when applied as per label directions. And once dry, they do not affect kids and pets in the same manner as do the W&F granules nor are they easily tracked into the home. But I would encourage you to attempt the manual removal first if the weed problem is not overwhelming - it is the most efficient and thorough method of weed removal and has NO negative impacts on you, your kids or the environment.