Search Challenge (8/27/14): What are these plants?

When I go out for a run I usually carry my phone or a camera, just in case I find something odd, peculiar, or spectacular.  It's a quick matter to grab the phone and capture the odd plant, animal, street sign, or atmospheric condition that I'd like to understand.  Then, when I get back to my computer I can look up the things I've captured and get a bit more of an inside story about where I'm running.  

This week I found a few amazing things that I'd like your help in identifying.  The Challenge is the same for all three:  What IS this?  And what can you find out about it? 

1.  I found this under a redwood tree in a lawn at one of the Google buildings.  I visited here every day for a week, and took this series of pictures over a couple of days.  It's shady here, but as you can see, it's just the lawn under the canopy of the redwood.  What ARE these things? What's the genus and species name?  

2.  Here's another thing I found sticking up out of the soil in my garden.  This is a particularly well-watered section of the garden--you can see the green beans growing in the background.  Just before I took this picture, the brown parts at the tip were covered in flies.  I know why, because it smelled terrible--a bit like rotting meat--perfect fly attractant.  Unfortunately, I only got one good picture.  I took several, but it was in a somewhat difficult to reach place, and this was the only one in good focus. It's about 5 inches long, and seemingly appeared overnight.  What IS this thing?  (And should I be worried about it?)  

 3.  While running through the Stanford Industrial Park (where HP headquarters, Varian, Xerox PARC, and a bunch of Silicon Valley research labs are located) I found the bush below covered in red berries.  Each berry is around 1 inch in diameter, and the bushes themselves are used as hedges.  It's an attractive plant, and I can see why you'd plant long stretches of this between buildings.  Oddly, I've also seen this plant grown as a tree with a trunk planted as a decorative planting along sidewalks.  And if I recall correctly, I remember there's some connection with Madrid.  What kind of bush/tree is this?  And what's the connection with Madrid? What's the genus/species name? 

  

As always, you can click on the picture to see the larger, more detailed version of the image.  (And no, there's no useful metadata here in the EXIF of the images.)  

If you would, please let us know HOW you figured out the answers.  What tools did you use (if any)?  What search queries worked for you?  And what sidetracks did you take (and then get out of!).  

I hope these plants are exotic enough for you.  I have to say that I was surprised by each in my searches, and I hope you find this interesting as well.  

Search on!