Miles mentions that grid 334 (where they are building the Swan) is hostile territory. This is why Radzinsky freaked out when Sayid saw the plans for the Swan.
Richard and the Others know everything that's going on on their island. They are either letting the constuction happen or biding their time before they sabotage things.
The timer in the Swan had hieroglyphics built into it, so:
The Others were somehow involved in the construction of the Swan, or...
The DHARMA Initiative have knowledge about ancient aspects of the island's mythology.
Chang examined him in the urge of finding electromagnetic residues, then made sure his corpse is destroyed, in the light of his discoveries.
Alvarez is brought to the The Orchid so it would seem like the accident happened at the Orchid construction site instead of the secret Swan construction site. They are trying to keep the Swan station a secret.
The body was not brought to the Orchid, but to Pierre Chang. Pierre has the same ability as his son Miles; he can find out the reasons why Alvarez was killed.
Horace said over the phone to Chang, "If it was caused by the electromagnatism, we need to know." The body was brought to Chang becuase they wanted him to confirm the cause of death without raising suspicions. They didn't want to ask any of the medical staff and freak them out.
Tom killed Felix in order to prevent Widmore from getting this information and to use it to get Michael to return to the island.
Felix was carrying the information to Widmore, Tom killed Felix and that is how he found out about Widmore's involvement with the conspiracy. He then uses the information to prove to Michael the validity of his claims and presumably told Ben.
The Numbers engraved on the Hatch door
Given Hurley's connection to The Numbers, he will be present when the code is programmed and he will select the code.
This was the inception of 'the numbers'. A random designation given to a new building. Something now happens that causes these numbers to be ingrained in to fabric of the Lost universe.
The numbers originate as a Serial Number. A Serial Number is used to help locate and track items. It is possible that the numbers being broadcast on the radio signal in the past is actually an attempt at a distress call to help locate DHARMA survivors from after the purge.
The numbers being broadcast are not a distress call. They were originally broadcast to Hanso Foundation headquarters from the beginnning, as stated in the Sri Lanka Video.