What is Russell's motive when he started examining the Bible with a group of bible students? Did he intend to form a cult and to mislead others?
Russell appears to have been a thoughtful young man who had his faith shaken when an atheist bested him in an informal debate. He stumbled upon the Adventist movement while still a teenager and eventually bought into it hook line and sinker.
There's little question that he was sincere in the beginning. The book, The Divine Plan of The Ages positively drips with the optimism and enthusiasm of a true believer.
There is no evidence that he intended to form a new religion, but this was likely the unavoidable consequence of the message he promoted.
But he later set the date of christ's parousia at 1874 and then change it to 1914.
No. Russell bought into the 1874 date after the fact. And the change to 1914 happened in the 30's, well after Russell's death. Rutherford was running the show at this point.
As a general observation, It is a peculiarity of human movements that starry-eyed dreamers are followed by a hard-fisted pragmatists. Orwell illustrates the phenomenon humorously in the novel, Animal Farm.