Can Stardust Dragon's effect stop Hyper Synchron's effect to remove the synchro summoned dragon from play at the end of the turn if so does stardust keep the 800ATK increase?

no it does not because stardust only stops effects that "destroy" a card(s) "remove" is different and therefore stardust cannot negate the effect

Also you can get a card called divine wrath in a pack and negate it.

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[Kaizoku]

-Stardust Dragon/Assault mode can, Stardust Dragon can only negate destruction.