Short answers, pulled from the story.
The Stockton and Darlington Railway officially opened on the 27th of September 1825. The first train carried between 450 and 600 passengers and reached speeds of up to 15 mph on its journey from Shildon to Stockton.
The Stockton and Darlington Railway was the world's first public railway to use steam locomotives. Its 1825 opening was widely seen as proof that steam railways could serve as an effective means of public transport, and it directly influenced the construction of further railway lines across Britain.
Edward Pease, a Quaker businessman, was the principal financial backer, subscribing £7,000 and giving the line its informal name "the Quaker line". George Stephenson was appointed Engineer in January 1822 and advocated the use of steam locomotives. Timothy Hackworth served as locomotive superintendent and built the Royal George at the Shildon works.
Locomotion No. 1 was the first steam locomotive used on the Stockton and Darlington Railway, built at Robert Stephenson and Company's works at Forth Street, Newcastle. It left the works on the 16th of September 1825 and hauled the inaugural train on the 27th of September 1825. The original locomotive is now preserved at the Locomotion Museum in Shildon.
The S&DR opened a branch line to Middlesbrough in 1830 to access deeper water on the Tees for coal exports. Thomas Richardson, Joseph Pease, and Edward Pease formed the Owners of the Middlesbrough Estate and developed the land around Port Darlington. Middlesbrough had only a few houses before the railway arrived; a year later its population exceeded 2,000.
The Stockton and Darlington Railway was taken over by the North Eastern Railway on the 13th of July 1863, transferring 200 route miles of line and about 160 locomotives. Under a clause in the amalgamation act it continued to operate as the independent Darlington Section until 1876, when it became the NER's Central Division.