The plan below of what was then called Birkenhead Iron Works may help with identifying the various buildings shown in the picture, as long as you bear in mind that the lithograph only shows the yard from Monk's Ferry at right to No. 4 Graving Dock at left - the south end of the yard is off the picture to the left.
The building on the right is indeed the Monk's Ferry Hotel, as shown in the other plan below, which dates from 1844. The Hotel was built by James Bryans in 1837 in anticipation that the Chester to Birkenhead Railway, whose construction had just been given the go-ahead by Parliament, would require a riverside terminus to link up with the ferry to Liverpool. In the event, the railway initially only ran as far as Birkenhead Town Station (at the end of Grange Lane) and was not extended to Monk's Ferry until 1844. Monk's Ferry remained the main rail-ferry interchange until the opening of Woodside Station in 1878.