I’d mention “I Have No Mouth and I Must Scream” but that probably doesn’t fit the realism requirement.
Ted Chiang’s novella “The Lifecycle of Software Objects,” available online http://subterraneanpress.com/index.php/magazine/fall-2010/fiction-the-lifecycle-of-software-objects-by-ted-chiang/, sounds almost exactly what you are looking for. Well, bullets 1-3. Spoiler: doesn’t really get beyond that. I think one of the reasons it is hard to find what you’re looking for is that in a reasonable timescale you can really only do some of your bullet points.
At any rate, even if it’s not exactly what you’re looking for, Ted Chiang is awesome and everyone should read him anyway.
Wiki article: Artificial intelligence in fiction.
TVTropes: Robot Roll Call Index of many, many AI-related trope pages.
Explore!
Two more I’d add to this list are Greg Bear’s Blood Music and The Metamorphosis of the Prime Intellect, by an “amateur” author named Roger Williams. You can read the latter online. How its AI evolves is always how I figured my Commodore 64 would do things when I was in grade school, if I could just write the correct code to start it down the process!
Reminded of this thread because the cover story of Time Magazine this week is on the concept and possibility of a technological singularity.
R.U.R. is from the 20s but it gave us the word robot which is cool and touches on questions of robotic autonomy and what makes something human.
Robert Silverberg: Tower of Glass
Yea but faster doesn’t necessarily mean smarter. The first computer had the IQ of a rock. Current computers are much faster, but still have the IQ of rocks.
Consider it another way. If you simulated a cat’s brain perfectly at 900x normal speed would it ever likely crack String Theory?
String is not a theory. String is a toy. 
Reading that was time very well spent. Thanks 
Ah, yes. I read that just a few years ago. A bit dated now, 30-some years after it was written, but still pretty interesting. By the end you’ll definitely be wishing someone had thought to install the Three Laws in those androids.
Ian MacDonald - River of Gods and Cyberbad Days. Great books.
This was the book I came in to mention. Does Stross still have it up for free download?
How about The Adolescence of P-1. A bit dated (it’s from 1977) but it does examine the creation of and reaction to an AI and it tries to be “realistic” about it.
Artificial Intelligence yes, but not robots in the modern sense, and otherwise pretty much exactly what you want: R.U.R., a Czech play from the early 20s. Also considered the first use of the word “robot”, actually. It’s a play, but quite a good read.
See post 45.
Doh! I read the post before and the post after, i ran a search for Universal Robots and RUR, but not R.U.R. Oh well, its pretty dang close to’ the OP and deserves another mention.
Well, points 3 and 4 are the plot of Asimov’s Bicentennial Man. Don’t know if you’ve read it; it’s sometimes included with his Robot stories. It has the Three Laws but none of the cutesy detective stuff. I see your point about some of his Robot stuff, but if you haven’t read Robot Dreams (the short story) it’s point 3 in just a few pages. Frederik Pohl’s Midas World is a mildly dystopian look at post-scarcity economics, and is related to your points 3, 4, and especially 5.