Trading special items

No if you have at least 1 Sunflora and Bellossom each.

I have already thrown away lots of evolution items. Honestly, once you have done the necessary evolves, they are mostly useless. The mons requiring evolution items are generally not that great.

I would throw away something else instead of an evo item. Razz berries, regular pokeballs etc.

And if you are running out of storage that either means you 1, need to catch more pokemon and use up some pokeballs or 2 battle some gyms and use up some revives and potions.