Learn Russian: Посмотри, кто-то несёт огромный гриб! - Look, someone is carrying a huge mushroom!

Несёт is the unidirectional verb for carrying on foot. It is used here because the person is carrying the mushroom in a single direction right at this exact moment (as signaled by 'Look!'). Носит would mean carrying it aimlessly, making multiple trips, or carrying it as a habit.

Since the mushroom is being carried, shouldn't огромный гриб change its ending for the accusative case?

It actually is in the accusative case! Because гриб is a masculine inanimate noun (not a person or an animal), its accusative form looks exactly the same as its dictionary (nominative) form. The adjective огромный follows the exact same rule.

Why use кто-то for 'someone' instead of кто-нибудь?

Кто-то is used when a specific, existing person is meant, even if the speaker doesn't know who they are. The speaker sees a real person carrying the mushroom right now. Кто-нибудь is used for a hypothetical person ('anyone'), like if you were asking 'Is anyone carrying a mushroom?'

Could I say Смотри instead of Посмотри?

Yes, both work here. Смотри (imperfective) is very common for 'Look!' or 'Watch!' to draw attention to an ongoing scene. Посмотри (perfective) is like saying 'Take a look!', focusing on the quick, completed action of turning your eyes to spot the specific thing being pointed out.