OK so my answers were guesses based on the material as I remember it. But then I realized hey! I have the official Lost encyclopedia. Some answers from there:
Not specifically mentioned, in either case. But I think using the Lamppost or donkey wheel are reasonable options for Ben. And given Jacob’s not interacting with anyone but Richard, I think it’s reasonable to surmise that he could get off the island through his special powers. Which means, in turn, Hurley could leave the island with his new superpowers.
Not specifically mentioned. But our only options are the last remaining vestiges of DHARMA, some sort of trust fund left by DHARMA, or the Others having taken over DHARMA, or more specifically Hawking in secret.
[QUOTE=LostEncyclopedia]
All of the DHARMA Initiative supplies were stored in a warehouse in Guam. DHARMA’s Lamp Post station, which was based in Los Angeles, had an automated system that periodically alerted the warehouse team when another pallet drop was required. The coordinates were then sent to the warehouse, detailing where the drop-off needed to occur.
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[QUOTE=LostEncyclopedia]
After the Purge, the Lamp Post was abandoned but the automated coordinates it generated and the subsequent drops continued until 2010.
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Originally I thought since Ben showed up, the Others must have taken over DHARMA. But I have an alternate theory - given that the Swan was so important, some sort of trust fund could have been set up to keep it’s operation running into perpetuity.
OTOH, per my original theory:
[QUOTE=Lost Encyclopedia]
After Eloise left the island post-Incident to give birth to her son Daniel, she became one of the Others who protect the island from a distance. Due to her soured relationship with Charles Widmore and his subsequent exile from the island after she left, Hawking made it one of her goals to keep the Lamp Post a secret from him, especially as he obsessively sought a way back. She took on a caretaker’s role for the station.
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So, obviously, the Others took over some of Dharma off island, and more specifically, Hawking took over the Lamppost (and maybe the connected supply station) in secret. But also, it seems, Dharma still existed in some capacity for at least a few years if only to take care of the Swan (hence Kelvin Inman’s recruitment to the Swan).
[QUOTE=LostEncyclopedia]
In the early 1990s, Inman left the army due to a guilty conscience and joined the DHARMA Initiative as a way of atoning for his sins. He eventually ended up manning the Swan station along with Stuart Radinsky
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[QUOTE=LostEncyclopedia]
Hurley’s first task was to return Desmond home safely home to his family, which Ben helped him achieve
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[QUOTE=LostEncyclopedia]
Desmond had done his part to save the island and help Jack move on as destined and his reward was to return to Penny and Charlie with Hurley’s help.
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[QUOTE=LostEncyclopedia]
[After the Purge] While the DHARMA Initiative attempted to recruit new members to rebuild the island community (especially to man the Swan), they were never able to regain their pre-Purge presence and the Others moved into their former compound.
[/QUOTE]
Yeah, looks like some Dharma operations were taken over by the Others, The Lamp Post and maybe resupply station were secretly taken over by Hawking, and some Dharma operations survived mostly to keep the Swan alive.