1) One of his Mystery Cards, namely "The Stars are Right!", says:
When this card enters play, move each Clue on the game board to the nearest Sea space.
Does it mean that, after the card enters play, EACH TIME a clue is spawned, I have to move it to the nearest sea space?
No. Take the rules of this game literally. The effect happens when this card enters play. Any clues spawned later are spawned as normal (and can be used to solve the mystery).
2) After Cthulhu awakens, the "Madness from the Sea" section says:
When an investigator moves ONTO a space containing an Eldritch token, he becomes delayed, loses 1 Sanity and places 1 Sanity token on this sheet.
A pretty nasty effect. Does it mean that I can't pass THROUGH a sea space using a travel ticket? Or that Silas' ability doesn't work?
Yes, once the seas start getting clogged up by Eldritch tokens, sea travel becomes slower and more dangerous. But note that, when you become delayed during the action phase, you just lose your actions for that turn (you are not delayed in the next turn). So what people usually do is do their first action normally, then move into the sea as their second action. They lose 1 sanity, but they haven't got any more actions to lose so the delayed bit has no effect.