The style recalls some 11th-12th century Tibetan brass statues with an equally tall chignon, rigid pose, flat billowing scarf, on a similar type of lotus base. Although classed as 14th century, it may be a more recent imitation.
PS: Some time after this was posted, the museum website labelled this piece ’19th century’.
Again, the style recalls 13th-14th century Tibetan works representing Jambhala and there is nothing at first sight to indicate that this was made in Mongolia. In fact, it may have been found in Mongolia but made in Tibet.