Learn Russian: Сейчас гид ведёт группу в древний замок. - Now the guide is leading the group to the ancient castle.

The word Сейчас (now) tells us this action is happening right at this moment, moving in one specific direction toward the castle. For a single, in-progress trip, we use the unidirectional verb вести (here conjugated as ведёт). If the guide led groups there every day, we would use the multidirectional verb водить.

Could we use a form of везти (to transport) if the guide is taking the group somewhere?

You would only use a form of везти if the guide were transporting the group in a vehicle, like a tour bus. Because вести is used here, we know the guide is leading the group on foot.

Why is the word for group spelled группу here?

The group is the direct object of the sentence because they are the ones receiving the action of being led. Since группа is a feminine noun, its -а ending changes to -у to form the accusative case.

Why don't the words древний замок change their endings to show destination after the preposition в?

They actually are in the accusative case! After the preposition в indicating motion toward a destination, we use the accusative case. However, for masculine inanimate objects (things that aren't alive, like a castle), the accusative form looks exactly the same as the dictionary (nominative) form.