"They reported, almost offhandedly, that 1/3 of solar-type stars have sub-Neptune mass planets with periods of 50 days or less. That’s the most important planet news since the discovery of hot Jupiters."

Can sub-Neptune mass planet with periods of 50 days or less support life.

If Neptune orbited our Sun at a orbit which had length of 50 days, could it have a possibility of lifeforms?
And if not such a planet, what about any moons it had.

In other words Mercury has an orbital period of about 88 days, one could make a good guess that if Neptune was in Mercury's orbit it would be too hot to support life. But perhaps that guess would be wrong.

If Earth had Neptune's mass: 102.43 10^24 kg instead of
Earth's: 5.9736 10^24 kg, what would Earth's atmosphere be likely to be composed of?

And instead forming at Earth orbit and with our current Moon, etc, suppose Neptune was simply transported to Earth orbit; would that planet change significantly over billions of years- would it lose it's Hydrogen and Helium atmosphere?

How close to the Sun does a Neptune need to get to start to lose it's Hydrogen and Helium atmosphere. Or does it's gravity and sheer size of it's atmosphere mean that in terms of a few billion years it will retain most of it's atmosphere- or could even gain atmosphere over time. If you put a Neptune mass planet with no atmosphere at Mercury distance does it gain atmosphere from the Sun?

Hydrogen and Helium are the most abundant elements in this Universe. It seems to me that at some mass greater than Earth's, the planet atmosphere should be dominated by H2 and He. How massive does a planet need to be?

Taking Neptune and putting at Earth orbit, and standing on it surface, one isn't going to able to see the Sun. It will be pitch black. So, pitch black but what would the average "sea level" air temperature be?
Helium isn't a greenhouse gas, nor is H2 as far as I know. There is more atmospheric "surface area" to radiate heat.
Now, if you raise your elevation so you are around 1 or 2 atm, you going come out of the inky darkness into bright sunlight, and below you, will be [I suppose] a bright blue planet. Now at 1 atm, what is the air temperature?

I would guess the temperature would be somewhere below freezing.
One way to look at it is that Neptune would be a black body- a perfect black body. We would see a blue planet, but that only because the reflected light is blinding us. If we go down in elevation, as it becomes dimmer, the planet would become darker until it was completely black.

So, how close to the Sun would Neptune need to get so the air temperature at 1 atm was say 70 F?
Now at a distance from the Sun, in which Neptune is 70 F at 1 atm, the lower elevation atmospheres will be a inky black scorching oven. Just as Venus at 1 atm is somewhere around 70 F. That's not my point. My point is that I imagine it will be much closer orbit than a Venus orbital distance.

So we have that aspect.
Next question is concerning the orbit's eccentricity- the higher the eccentricity the faster the orbital period, and the longer the planet spends further from the Sun.

As an extreme example, suppose a orbit which went closer than Mercury and as far as Jupiter.

Now shortest orbital period of comet I could find is Comet Encke:
http://en.wikipedia.org/wiki/2P/Encke
Orbital period: 3.30 years
Perihelion distance: 0.3302 AU
Aphelion distance: 4.11 AU

Mercury's average distance is .38 AU
And Jupiter's is 5.20 AU

Now if you kept Encke perihelion distance the same, but reduced it's aphelion distance to earth orbital distance, it's orbital period will reduce significantly [certainly less than 1 year].
LONEOS is pretty close:
"As shown in this diagram, JG6 crosses the orbits of Venus and Mercury, passing less than 30 million miles from the Sun every six months. The approximate average orbital speed of this asteroid is more than 30 km/sec, or 67,000 miles per hour. Depending on their locations, the asteroid may pass as close as 3.5 million miles from Earth and about 2 million miles from planet Mercury."
http://www.spacedaily.com/news/asteroid-04g.html

So, this rock has about 180 day year.
Anyways, it would possible to have a orbit which had 50 day year, with a perihelion closer than 30 million miles from Sun and somewhere between Earth and Venus orbital distance at aphelion.
And the average planetary temperature would correspond to orbital distance of between Earth and Venus.