Skyrim does need the Empire. Most of Skyrims food and trade comes with the Empire.
What? I saw tons of farms in Skyrim, and they seem very self sufficient. I think you're a bit confused. Most of the Empire's trade comes from Skyrim atm.
Did Skyrim even get touched in the Great war? How would the Nords react if the Altmer invaded windhelm?
They would take it back fast.
Not only that, but they'd march out and kill every elf they saw until they reached alinor.
If the Empire had waited instead of Acted, Skyrim would have been reached by the Altmer.
The empire waited for 150 years instead of acting. The current situation is a direct result of them not taking any action.
Who are the Stormcloaks really helping by attacking the Empire? Themselves or the Thalmor?
Everyone. The ban of talos is why the world started to end. Talos holds back the next kalpa and NEEDS worship and recognition. Not just privately either, in the world of TES symbolism is extremely important. The removal of Talos from the nine reduced Talos's power greatly, even if they still privately worshipped him.