Um, we ARE talking about sustaining life in Outer Space? I DID SAY "nothing in the mind of Man", not 'nothing in the mind of God'.

Yes, I DO know about the fact that cosmic rays are stopped by our planetary atmosphere.
Several miles DEEP planetary atmosphere.
But this is not exactly a practical means for using as radiation shielding when you are LEAVING said planetary atmosphere.
The atmosphere is also exceptionally low density, which is why it needs to be so thick. It shows that cosmic rays can be shielded against for biological purposes, and allows you to calculate the amount of material that's needed, which works out to about 1,000 grams per square centimeter of shielded area, or ten meters (1,000 centimeters) of water. The main problem with that is that it would be very expensive (hundreds of billions of dollars at current launch costs) to launch that much water into space, not that it couldn't be done or that it would pose any particular engineering difficulties. And that's a problem any space efforts would run into (and one which would be mitigated by a large, reusable spacecraft, too--you only have to launch that water once).
Anyways, even without any shielding at all you're only exposed to half a sievert per year of cosmic rays in free space, and half that much on a planetary surface. Not exactly the greatest for your health, but it won't immediately kill you or anything, just raise your risk of cancer and other aging-related diseases. Plenty of astronauts would go--have said they would go--even so, knowing those risks.
Its not impossible, provided you do the construction in outer space, where gravity is no problem. Oh wait...cosmic rays.
The best shielding materials are mostly liquids, which can be easily pumped. What problem? You just launch the habitat module without the shielding material onboard, then fill it up in space. It can all be done by robots with minimal if any human presence (take a look at operations around the ISS for an example, particularly the Progress missions).
Again though, such a vessel needs to be constructed in outer space. Which would require space construction and service dockyards in outer space. Which would mean people being exposed to the radiation dangers on said space dockyards for the many years it would take to construct them AND any deep space vessels they construct.
You mean...like the ISS? Which has been in space for sixteen years? And constantly crewed for fourteen?
You're also seriously misunderstanding what something like this would look like. Labor in space is extremely expensive, so there's a huge premium on doing as much on the ground as possible and automating everything else. An interplanetary spaceship would probably be "assembled" by docking or berthing separate, modular components together, then adding any fluids or other consumables if necessary, with only a small amount of in-space human labor mostly dedicated to checking out the spacecraft and setting up its habitat areas. There would not be any concerns about radiation sickness or permanent problems from bone or muscle loss, especially since orbital crews would probably be rotated if they were in orbit permanently, like ISS crews, instead of being sent up only as necessary.
Not to mention that those dockyards would have to be built in geo-synchronous orbit if we don't want to see them coming down before they (never mind any deep space ships) even finished being constructed.
Er...no. Never mind the fact that geosynchronous is very hard to reach, there's no problem with putting construction facilities in low Earth orbit. There are these things called "rockets" that can counteract atmospheric drag, you know? The ISS, which is at least as big as any "spaceyard" has, as noted, been in orbit for sixteen years just fine, and it's been largely complete for more than five without "coming down". The same goes for basically every space station. The only ones that have "come down" have been ones that were basically abandoned and left to orbitally decay on their own, which is obviously not something you would do to an operating "spaceyard".
Then there's the cost of the natural stress factors of a rotational drive system for the space stations/dockyards/deep space craft. If the astronauts/cosmonauts are feeling the gravity, so is everything else.
Rotational...drive system? You mean the rockets or electric motors you use to set them spinning? And, you know, we do have quite a bit of experience with building structures subject to those sorts of forces on Earth.
Artificial gravity is practical, it mostly hasn't been tried because the space stations people have actually built have been designed to study microgravity, which obviously a rotating station doesn't. It would be an obvious feature for an interplanetary spacecraft.