The third example uses a rather unusual sense of 'let loose':
M-W has an example of the intransitive use of 'let loose' (a multi-word verb):
let loose [verb] (2): to produce (something, such as a cry) in a sudden and forceful way
The crowd let loose an enormous groan when the pass was intercepted.
She let loose (with) a scream.
'She let loose with a scream' is the intransitive example. M-W does not add a caveat.
Wiktionary is clearer:
let loose (1) (transitive, idiomatic) To free; to release from
(this is the usual sense)
... the unholy ambitions which let loose this horror ...
(2) (intransitive, idiomatic, sometimes followed by with or on) To
shout, make a loud sound, or perform a sudden, vehement action; to
behave in a raucous, frenzied manner.
He set his teeth, and let loose with a fury before which nothing could stand; and Maurice was forced back step by step until he was
almost up with the wall.
'Dogs are let loose' is just the passive transformation of 'They let the dogs loose', Wiktionary sense (1)
'Ellen was laughing like a child let loose in a sweet shop' uses a reduced relative clause (from 'Ellen was laughing like a child that had been let loose in a sweet shop').