(i) When X cards are discarded from your deck, they enter your discard pile one at a time so the last card discarded is now the top card in your discard pile, right?
Yes. Cards are discarded from your hand or deck one at a time in the order in which they are discarded. So the last one discarded would be the top one of your dicard pile.
(ii) Are you allowed to browse your hold without any search effect when playing the Black sails agenda? I can't find anywhere in the rules insert anything in either direction.
The information that has been spoiled thus far shows that The Hold is information that is to be hidden from your opponent (Naval Reinforcements says to "reveal" the character). However, it is very telling that with the plot, you "reveal" the character (rather than searching
for the character and then revealing it), and that with the Agenda, you "choose" a card from The Hold (rather than searching
The Hold for a card). That means that while the contents of The Hold are hidden from your opponent, they are not hidden from you. This implies that you can look through The Hold, the same way that you can look through your plot deck or through the cards you have in Shadows.
It's probably a little unsporting to pick up The Hold immediately after it has been created and spend the next 10 minutes looking at every card, but it actually makes a lot of sense to peruse it immediately in order to get a feel for how you need to play and how soon you will need to dip into The Hold. For example, it's important to know if your only Maesters ended up in The Hold so you know whether to play At the Gates or Naval Reinforcements as your first plot.
(iii) In order for you to search for a card you must win a challenge in which you had a naval attacker. This means that the attacker must have been declared using the new naval mechanic (thus having to effectively attack with two characers, one normal attacker and another one naval attacker) and the response cannot be triggered by a character with the matching challenge naval enhacement icon attacking normally, right?
No. The "After you win a challenge in which you had at least 1 Naval attacker…" language is something that is defined at the resolution of the challenge. Once you resolve the challenge, the game makes absolutely no distinction on how
the character with the Naval Enhancement got into the challenge. The designation "Naval attacker" means "attacking character with a Naval Enhancement." So it doesn't matter whether the character was declared in the standard framework event or using the Naval enhancement mechanic; you just have to end the challenge with an attacking character who has the Naval enhancement.
This is a corollary to the fact that a character that is removed from a challenge is considered to have never participated in that challenge at all. So, for example, if you used the Naval enhancement to declare a character as an attacker, and that character is subsequently removed, that character is not considered to have participated in the challenge at all. So it is the fact of participation at resolution that matters in general in this game. This sets up the above conclusion that it is the fact of participation that makes a character a "Naval attacker," not the exact method by which it was declared as an attacker.
(As a side note: the assumption, of course, is that the character has to have a Naval enhancement on the challenge icon corresponding to the challenge type. For example, say you have a character with the power and military icons, but only the military icon has the Naval enhancement. You win a power challenge with that character. It is not immediately clear without something official from FFG whether or not you had a "Naval attacker" in that power challenge, although the assumption seems pretty clear that you did not have a Naval attacker in the power challenge, although that same character would have been a Naval attacker in a military challenge, whether he used the enhancement to dictate the timing of being declared an attacker or not.)
~ Aren't you gald you asked?