Learn Italian: Che capolavoro maestoso viene esposto nel museo! - What a majestic masterpiece is exhibited in the museum!

In Italian exclamations, che connects directly to the noun. You never use an indefinite article (un, una, ecc.) after it. So, 'What a masterpiece!' is simply Che capolavoro!

Could I use Quanto instead of Che here?

No. Quanto is used to emphasize verbs, adjectives, or quantities (like 'How much' or 'How many'). Because you are exclaiming about a specific noun (capolavoro), you must use Che or Quale.

Why does the sentence use viene esposto instead of è esposto?

This is the dynamic passive voice. Using a conjugated form of venire instead of essere emphasizes the action of the artwork being placed on display, rather than just describing its static state of already being there. It translates closer to 'gets exhibited' or 'is being exhibited'.

Does the adjective maestoso have to go after the noun in an exclamation?

Not always, but it is the most natural order. In Che exclamations, you can place the adjective before the noun for a more poetic or dramatic effect (Che maestoso capolavoro!), but putting it after is the standard, everyday way to say it.