[Pitchwife]

This is getting rather complex, so, one thing after the other:

1. Seasons
If I remember my astronomy correctly, seasons are caused by the tilt of the Earth's axis, which makes the two hemispheres receive more or less sunlight in longer or shorter periods at different points of our orbit around the Sun. I guess you can explain seasons in a geocentric Flat World model by having the Sun move around the Earth at varying distances - but no Sun, no seasons.
How did plants in Middle-Earth grow without sunlight? Intriguing question... To be sure, Nogrod did well to remind me early in this thread that Tolkien was creating a mythology (not writing science fiction), and any attempt to make it agree with modern science is bound to run into problems sooner or later (as the Professor found out himself). Hence, Legate, your idea of things being 'just the way they look' (no cells, no microbes, no photosynthesis) does have a certain charm. On the other hand, Arda is supposed to be our world, and I can't help thinking that the plants and animals must have been more or less of the same kind as ours.
Anyway:

you make the Sun and Moon the things that caused the plants to wither fast and grow fast. Not sure if that's the right thing to claim.

I don't see why not. Leave alone the Moon, but I seem to remember several statements by Tolkien (not that I can find a quote right now) saying that all things in Middle-Earth changed swifter in the Age of the Sun. Remember Letter no.131 to Milton Waldman:

A marked difference here between these legends and most others is that the Sun is not a divine symbol, but a second-best thing, and the 'light of the Sun' (the world under the sun) become terms for a fallen world, and a dislocated imperfect vision.

2. Hunting, Gathering and Agriculture
We know that the Elves practised agriculture. The Silmarillion mentions the fields of Valinor, gold beneath the tall wheat of the Gods, and the feast during which Melkor and Ungolianth killed the Trees was a harvest festival.
We also know that they hunted. Celegorm, for example, was a great hunter who often followed Orome's horn in Valinor - not just for a pleasant ride, I suppose (remember Huan!). In Middle-Earth, Thranduil's folk in Mirkwood hunted as well, see The Hobbit.
And we certainly know they did breed in Valinor! Finwe's children were born there, and their children too. Laws and Customs among the Eldar tells us, however, that the Elves had few children, and those mostly early in their married lives, so I don't think they had an over-population problem.

3. Death and Arda Unmarred
This is still the question that puzzles me most and made me start/revive this thread in the first place. I think I've finally found a quotation myself that demolishes my initial misconception (from the Athrabeth, Finrod speaking):

'For you speak of death and [Melkor's] shadow as if they were one and the same; and as if to escape from the Shadow was to escape also from Death.
But these two are not the same, Andreth. So I deem, or death would not be found at all in this world which he did not design but Another. Nay, death is but the name we give to something that the has tainted, and it sounds therefore evil; but untainted its name would be good.'

So it seems that death (or something like it) was part of Eru's original design after all - and we're all free to try to imagine what death untainted would have been like. Anyway, I take it Finrod is talking about death in general, not just the death of Men, but that may be just me - sorry, Legate, I find the idea of a world where nothing dies but Men rather chilling. Wouldn't it be even harder to accept and come to terms with death in such a world than it is in ours? To quote two lines from our German poet Günter Eich (my translation):
Who would want to live without the comfort of trees?
How good to know they, too, partake of dying!