Number 4 is totally wrong.

"In order to be able to think up a hypothesis which has a significant chance of being correct, I must already possess a sufficient quantity of information" is obvious, following immediately from the mathematics of information. But that's emphatically not the same thing as "I obtain my hypothesis by applying a 'principle of induction' to generalize the data I have so far."

The way induction was supposed to work was that your observation statements served as the premises of a kind of inference. Just as one can use deductive logic to infer "Swan[1] is white" from "All swans are white", so one was supposed to be able to infer "All swans are (probably) white" from ("Swan[1] is white", ..., "Swan[N] is white") for sufficiently large N.

But there is no such thing as a "method of induction" which finds hypotheses for you. Consider those swans: In order to even write down the data we needed to have the concepts 'white' and 'swan', and something must have motivated us to look specifically at swans and note down specifically what colour they are. In other words, by the time we get round to actually applying our "method of induction" we must already have formed the very hypothesis that the method was supposed to return, or something close to it (like "all swans are some colour - perhaps white").

This becomes comical when we turn to GR:

Our raw, unprocessed 'sense data' comes streaming in: ("The precession of Mercury's perihelion looks exactly as if (long description of the mathematics of general relativity)", "The apparent position of this star as the sun moves in front of it changes in a manner that looks exactly as if (long description of the mathematics of general relativity)", "A clock aboard this high-flying plane runs slightly faster than one on earth, exactly as if (long description of general relativity)") ... and then, as if by magic, the Method Of Induction selects for us the appropriate hypothesis: (long description of the mathematics of general relativity).