Short answers, pulled from the story.
"Computing Machinery and Intelligence" is a 1950 paper by Alan Turing published in the journal Mind. It introduced the concept now known as the Turing test to the general public, proposing that machine intelligence could be evaluated through a conversational game rather than philosophical definition.
The Imitation Game in Turing's paper is a test in which a human judge converses via typed messages with a computer and a human, both of whom try to convince the judge they are human. If the judge cannot consistently tell them apart, the computer is considered to have passed the test.
Turing addressed the religious objection, the 'Heads in the Sand' objection, the mathematical objection (citing Godel's incompleteness theorem), the argument from consciousness (from Geoffrey Jefferson's 1949 Lister Oration), arguments from various disabilities, Lady Lovelace's objection, the argument from continuity in the nervous system, the argument from informality of behaviour, and the extra-sensory perception objection.
Turing focused on digital machines because they already existed in 1950 and because they are universal: a digital computer can simulate the behaviour of any other digital machine given sufficient memory and time. This meant that if any digital machine could act intelligently, then every sufficiently powerful digital machine could.
Turing proposed that a learning machine should start as a child-like mind, simple to programme, and then be educated through a system of reward and punishment. He compared this process to natural selection, with the experimenter's judgment playing the role of selection pressure.
Ada Lovelace argued that the Analytical Engine could only do what it was ordered to do and had no power to originate anything. Turing reframed this as the claim that machines can never surprise us, then disputed it by arguing that machines can produce unexpected results whenever the consequences of different facts are not immediately recognisable.