1. Nami sent the police after them, so it was something that was unsanctioned by adults, so no cars. Nika and Summer got to the cabin on their own steam as neither could drive. Also, a 15 year old can't go faster than a car for 6 hours on a bike. Even if the "old" home (do we know they moved, or is it just the decor and room we see of the "old house" an assumption?) was closer, it was in walking distance to the lake, which Nika can currently walk to and back before breakfast. Nami and Noji's confirmation of the cabin (Nami by calling Jane, Noji by asking if AMber really means that cabin) confirms Nika's story enough.
2. Can't be, because of the lake, currently a 15 min walk or thereabouts, which if they walked from their old house, they wouldn't walk further than an hour, especially as they talk about the beach being on the bus route, and the surfing thing with Zara, saying the beach is close... so at best the lake would be between the two houses, in walking distance from either, putting the cabin at least 5hrs 45min from the lake still.
3. Yes, this would be one way, but create the exact problem you describe.
4: A sensible solution - the cabin was simply where NIka and Summer ran away to and is only known to Nami and Noji after Jane finds them. But for Nika and Summer to run away jsut to have alone time before SUmmer's family vacation, they'd choose somewhere closer. 6 hours at 60km/hr by car (conservative, based on slow roads, mountains etc), 360km, which at 5km/hr hiking, would be 72 hours. I'm sure they could find somewhere for alone time closer. Take off maybe 2 hours most for the walking distance between the potential old home and the new one, we're still at 70hrs of hiking.
So 5:
This is the most likely answer, nailed it!
View attachment 4432602
Nika's Raziel. There's a chronoplast to solve pesky time issues as well as the Elder God, and there's the legacy of his predecessor to work out.