The sun wont just be "shut off" , not even an elder scroll can do that. The sun has been here for billions of years and will be for billions more. It is trillions of nuclear bombs going off at once. Plus, if you do shut it off, it will be a lot worse than plants dying like everyone is saying would happen. The whole planet, NO, THE WHOLE SOLAR SYSTEM, will freeze over before the plants would get a chance to die.

No. I believe that it will be an eclipse that turns everything red during the daytime. Then, all the pretty flowers won't die and everyone won't die a suffocating and excruciating death from being turned to popsicles (Vampsicles)

If it is permanent remain to be seen.

That would be a pretty big change to the world and for the rest if there's any more, hopefully there will be, TES games. I doubt it would be like that and the lore would be the dawngaurd succeeded. But it would be interesting for skyrim and to see how the npc's react to it

The sun there is not the same as the one here.

The Sun is nothing more but a hole created when Magnus fled the creation of Mundus back into Autherius. So it's not a star of gas giving of solar waves it's a big hole in the fabric of space where magic comes from. Closing the hole therefor is not the same as destroying the sun, it doesn't even compare as the "sun" will still be there, it just won't reach Mundus.

By the way, the stars you see at night are other smaller holes created by Magna'ge, spirits that followed Magnus but weren't as powerful as him. Those would still continue to work.

An eclipse can't happen. The sun isn't a thing, it's just a tear in the fabric of Mundus, when Magnus ripped through when he was escaping the formation of Nirn. If it was covered, the flow of magicka would be severly restricted. I'm not quite sure if the sun function the same as in the real world though. It may still give of solar rays that plants need (if you notice, all farms are outside, not inside) and that generate heat, but we can't be sure.

We can make an educated guess though.

This http://www.imperial-library.info/content/nirnroot-missive-0 mentions that during an earlier time when the sun was blocked out (during an erruption of Vvardenfell in the 1st era) most plants survived just fine. Nirnroot were effected though, so it doesn't seem that plant life needs the sun as much on Mundus as it does on earth.

Though this could be in part because the plants are magic, and blocking out light does not block out magic.

Then why are all farms outside? I'm sure it'd be more convenient to have all your crops protected from the elements, inside.

Also, the book says the other plants "found away". So, presumably, they do have some dependence on the sun's light, but only as much as that they can live without it temporarily.

I said as much, not that it wasn't needed at all My speculation would be that heat as well as things like rain do have a real impact on plant life, also building a shed to cover a farmland might be a lot of work and rather expensive in most situations. Magic probably plays a part too but actual sunlight doesn't seem to be necessary for plants to survive.