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I'm not the kind of person you wanted a response from since I know absolutely nothing, but I would imagine being an island, boats play a big role in keeping supply lines running.

I’ve been there on tour once, and I just looked at an online map to make sure I didn’t misremember. I also follow a guy on YouTube that talks about geology and has been focused on Iceland lately, so I think that makes me a complete expert.

Joking aside, the road to Grindavik is sort of out of the way, but it is the connector road between the south coast and the airport, so it’s like a 45 minute diversion to get to the airport from the south coast (and vice versa). And like an hour+ diversion if you’re going from the south coast to the Blue Lagoon/the geothermal power/hot water plant that provides power and heat to the airport and (I think) most of Reykjavik.
Unfortunately the power plant/Blue Lagoon is very close to the fissure, and it’s possible a future larger lava flow could damage them. (It is expected more fissures/flows will occur, but the location and size are unknown.) I’m sure both the civil engineering and tourism folks are working on spinning up alternative sites.

Grindavik, for what it’s worth, keeps bouncing between being evacuated and residents griping so much they get let back in. The Icelandic government has an offer on the table to purchase people’s homes in the town, so they move out. I think the plan is probably to abandon the town, since it’s possible this eruptive period could last hundreds of years. (Or not! We have no idea, really, just past data and informed guesses.)

Basically everyone gets evacuated from the affected area and are staying with friends and family in Reykjavík. Grindavík is a very small town compared to the rest of the world. The government has offered to buy properties from the ones who cannot return, since the erruptions have been going for a few years in that area and there's no sign of stopping.

To answer your question for the rescuers, researchers, and workers left in the area, once the eruption starts it's quite easy to predict the flow. Luckily there are a few other roads without the risk of lava flow, mainly due to lava diverting barricades. In case of emergencies they use helicopters.

Other parts in eruption risk zones would be similar, since it's just not worth it for people to stay in those areas and most people can stay with family. And repairs to the road are usually pretty quick when the eruption dies down.

Not Icelandic, but I've been following the situation closely.

This is an evolving issue. Grindavik, the town on the far side of this has been severely damaged by earthquakes and is currently surrounded by a berm that's (mostly) holding the lava flow back. The Svartsengi power plant is likewise protected by a berm and has had the pipes supplying hot water to Reikiavik damaged and repaired.

Geologist Sean Willsey has been providing outstanding coverage on the subject.

I'm guessing driving the other way around would help and boats. But I'm not an expert.