Habitable Worlds circling Red Dwarfs?

Here's an interesting short article (with very cool artist's conception and internal links) about the possibility of the existence of many, many habitable worlds orbiting red dwarfs (the most common type of star in the universe). 

The conventional wisdom has generally been that such worlds would be unlikely, mainly for two reasons: 1) they would have to be too close the star to be able to rotate with respect to it, in order to receive enough sunlight for habitable temperature (in other words they would tend to be stopped, with one face always to their sun, just as the moon is with respect to Earth); and 2) Red dwarfs flare all the time, and stellar flares are roughly the same dimensions no matter what the size of the star (no problem for a sunlike star over 100 million km from the planet, but a big problem for an "earthlike" planet only 4 or 5 million km from a tiny star; the flare could double the star's brightness and singe the planet). (Another objection is that photosynthesis is presumably a nearly universal process, and it only seems to work, chemically, with pigments like chlorophyll that maximize utilization of light well above the frequency of red light, but it can't be ruled out that there are other solutions to that particular biological puzzle; we only know about the optima for a planet with a yellow-star spectrum because that's where we live).

I don't see that recent developments really answer these potential objections, but it's interesting to see that astronomers are giving serious consideration to this, and actually collecting real data.

[Probably the first and only time I'll ever link to Fox News] .