The bridge at Delhi and the terminus became operational on January 1st, 1867.
The first attached scan is from the official reports to the Indian Secretary of State on May 24th, 1864, where the speaker reports to Lord Ripon that the bridge works at Delhi are still incomplete. Link to the full report: click here . These are records of the parliamentary proceedings in England.
The second scan is from the 1904 Administration Report on the Railways in India, which was an annual publication by the Railway...
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Board. This publication contains details of ALL the railway lines, dates of inauguration, doubling, tripling etc for EVERY railway line constructed in the subcontinent till that point, and also the finances, details about ongoing projects, surveys etc for that year. This report was actually published EVERY year till 1964, when IR stopped the publication. Some issues between 1893 and 1907 are publicly available on Google, while the other issues can be accessed in overseas libraries. This report mentions that the section to Delhi terminus was opened on January 1st, 1867. click here

You are right about the ferries. In the early years, trains were run on whatever length of the route was available. For example, even in the 1850's, when the railway connection was only available till Jamalpur, passengers would be carried by train till the limits of the railway, and from there, would take a tonga or a ferry along the Ganga till Allahabad, then switch to the railway between Allahabad and Kanpur and again take a road or river route till Delhi and Lahore. But these are not necessarily 'complete' trains. For the ferry and road transport arrangements had to be mostly taken care of by the passengers themselves. Some First class passengers or Elite Indian passengers would have the arrangements made by the railway company itself, but most would have to make their own arrangements. That way, through running of a train end-to-end on the route, is a better indication...
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of a consistent railway service, and usually marks the inauguration of a new, dedicated service.
If you observe the Report of railway construction in my earlier post, and the timetable from 1889 in my initial post, you will observe that the railway route between Calcutta and Lahore was completed by 1870. and a simple google search for a 'Calcutta mail' or 'Calcutta Lahore/Peshawar mail' in Google books, will give you several records for a Calcutta-Peshawar mail between 1870 and 1891 and these records will also clearly indicate that this was the ONLY mail service on the route. There was no separate mail train on the route. Some sectional coaches would run between Calcutta-Delhi and Delhi-Lahore, while the remaining coaches would complete a through run all the way to Lahore and beyond. The mail train that was inaugurated in 1865 (or 1866/67, but the date doesn't really matter) was ALREADY extended to Peshawar by the time the Kalka line was opened. There was no other mail train to be extended! It was only in 1891, that a second, faster mail train was introduced on the route, and this was the Kalka mail, which was introduced as a dedicated train just for the sake of moving people between Calcutta and Simla, the summer capital of the Raj.