Rules in question: Starrophytes are not considered to be characters or terrain. They do, however, affect line of fire and occupy squares as if they were characters, and they can be destroyed following the same rules for destroying blocking terrain.

Question One, re: affect line of fire and occupy squares as if they were characters
Does this mean that, if you are adjacent to one, you cannot make a ranged attack? (sans sharpshooter)

Question Two, re: can be destroyed following the same rules for destroying blocking terrain
Does this mean that anything that destroys blocking terrain can destroy them as well, or does this simply mean use the same rules but these things are not blocking terrain for other purposes

No, they do not have any effect on ranged combat (other than LOF).

As you already stated: "... and they can be destroyed following the same rules for destroying blocking terrain."

If it (be it SP, feat, whatever) destroys blocking terrain, that would be following the same rules for destroying blocking terrain, no?

What about Songbird's Punch Through!?

I'm assuming no, since: a) Starrophytes aren't actually blocking terrain and b) they are being removed, not destroyed, but I figured I'd ask, just in case.

Songbird's SP doesn't work on Starrophytes, no. But it isn't quite for the reason you state.

PUNCH THROUGH! specifically says blocking terrain markers. In other words, Barrier. If there is another game effect that would actually place a blocking terrain marker (like Foom's ability to create new terrain), the SP would work there, too. But normal blocking terrain or other things that are not blocking terrain markers (including Starrophytes) are not affected by the PUNCH THROUGH! sp.