The Matrix

[Makuza]

These are just my answers, I have no authority on this beyond anyone else's opinion

1. I understood that to be the hold of the illusion breaking away. If you consider that Neo's body is actually suspended in a gooey substance not unlike the "silvery stuff" he swallows, it might simply be that the hold of the Matrix's illusion on his perception is waning, but still twisting it. The same goes for the gagging sensation he obviously feels when the silvery stuff flows down his throat, which might be due to the machinery attached to his lungs etc.

4. Bear in mind that the first movie was not intended as the first of a trilogy (as far as I know). In my opinion, he is talking to the viewers of the film, including them in the plot as "blue pills".