Regarding the broad gauge it was BG for a very short time. A trial run with Broad gauge loco 2-2-2 Harpy, of the 'Firefly' class in August 1852 was made being met by civic dignitaries just after midday. After a 'beano' at the Queens Hotel the train left at 3pm.
On 14th. September, 1852 the Board of Trade inspector, Capt. Galton, only approved the new line as far as Bordesley Junction as the narrow/standard gauge line was not yet laid. This was completed a fortnight later. The uncompleted Duddeston Viaduct was not approved and as neither railway (GWR & LNWR), particularly the L&NWR as they were closing Curzon Street to passengers, had a new station in New Street and with pretty unfriendly relations between the two companies neither really wanted the viaduct link. Track was laid on the completed part of the viaduct, never used and was probably gone after 1880.
So eventually passenger trains began to arrive at the temporary Snow Hill on 1st. October 1852. There must have been good advantage to the new site as it became the principal station, nothing temporary at all.
In previous posts here much has been written, with great pics to accompany, about the former Great Western Hotel.
Prior to WW2 the GWR had grandiose ideas for reverting the use of the building back to being a hotel. From the descriptions it would have been a very 'well appointed' as they say in the trade, place.
However, it was not to be: the outbreak of the war halted it.