You are mixing up the meaning behind statement 2 and 3.
In statement 2, you correctly put the 95% uncertainty around your confidence interval. While in statement 3, the uncertainty is about your population parameter (mean).
An example: Suppose you study the shoe size of all Belgian people (= population) by taking a sample of 1000 persons and calculate a mean for this. The mean shoe size of the population is unknown then, but it is not gonna vary. If you had the tools and could perform a census, you could get the exact estimate.
However, there are an infinite different ways to sample 1000 persons from this population, and depending on your sample, you get a different estimate and thus a different confidence interval!
So the correct statements are the ones that imply that the 95% uncertainty is about the confidence interval: you either collect a sample and make a confidence interval based on this sample that contains the population parameter, or you don't, but the population parameter will not change!
Saying something like 'There is 95% uncertainty that the population parameter lies in the 95% confidence interval' seems to imply that the confidence interval is fixed, and the population parameter varies and might be situated in the confidence interval, while it is exactly the other way around!
Where goes the reasoning in your example wrong: In the very last sentence you say any single CI has a 95% probability to contain the true population mean. which is correctly about the confidence interval, but then you say this is equivalent to statement 3, which is not true! Statement 3 puts the uncertainty on the population parameter, and thus this final implication is not true: you have not implied statement 3 with statement 2 (luckily ;) ).