Learn German: Gestern ist ihm das heiße Backblech heruntergefallen. - Yesterday, he dropped the hot baking tray.

German often uses a 'dative of disadvantage' to show who is negatively affected by an involuntary event or accident. Literally, this translates to 'Yesterday the hot baking tray fell down to/on him.' This dative structure is the most natural way to express accidentally dropping something. If you said Er hat das Backblech fallengelassen, it sounds much more active and could imply he dropped it on purpose.

Since ihm is in the dative case, what is the actual subject of this sentence?

The grammatical subject is das heiße Backblech (the hot baking tray), which is in the nominative case. In this German structure, the tray is the thing actively performing the action of falling, even though the English translation makes 'he' the subject.

Why is the auxiliary verb ist used here instead of hat?

The main verb herunterfallen (to fall down) describes a change of location. In German, verbs that express a movement from A to B or a change of state always form their perfect tense with sein (in this case, ist) rather than haben.

Could I say runtergefallen or hinuntergefallen instead of heruntergefallen?