Why was the the Looking Glass station setup to connected to Penny's office?
We don't know where Penny, or more specifically, her father and his corporation, fits into the larger LOST conspiracy, but I think its safe to say that Ben is interested in anyone who's interested in the island. My guess is that the Looking Glass station was used as a spy station in addition to being a communication jamming station. It likely uses the island's strange properties to spy on the mainland. Thus the reason why Looking Glass was able to contact Penny; they'd been watching her office all along.
Why did the new arrivals flash back while everyone else is flashing
Because the new arrivals are flashing forward, at least relative to the Island's place in the time stream. It's been clear for a while that time on the island moves differently from that of outside; this was confirmed in Episode 3, Season 4 with the rocket experiment, as well as the teenage Walt's appearance on the Island at the end of Season 3. I don't think that travelling to the island is exactly the same as travelling backwards in time; it's more like it takes you out of the time stream. Think of the island as a rock in the middle of a river; once you stand on it, time just keeps slushing by.
Why does Naimi have a flashforward if she's dead?
This would seem to break the rule that flashbacks are only happening to people living on the island, but I think that death on the island isn't the same as death in the real world. Charlie demonstrates this in Episode 1 of Season 4. If we take him at his word, and I think we should, he's dead ... but he's also able to talk to Hurley. My guess is that if you die on the island, you end up being something like a ghost in the machine; a memory retained by the island that's able to interact with those who live on (as we've seen with Boone and a few others).
If the Island is unreachable, who keeps delivering supplies to the people there?
I think the supplies are delivered automatically from an undiscovered location somewhere on the island. I picture a huge DHARMA warehouse stocked with supplies and built into the side of some mountain. Drones periodically deliver supplies to the DHARMA stations.