The issue comes down to whether the passage is qualified as territorial waters or just exclusive economic zones and how the islands are connected to the mainland may determine that. Regardless, the US is pushing it because it's a useful way to get concessions on other issues. Like him or hate him, understanding and using that aspect of negotiation is one thing Trump was always very good at and in this case Mike Pompeo was the one putting it forward and lobbying other countries to see it their way.
Purchasing the F35s has been discussed here since at least 2007 when Russia was flying bombers into Canadian northern territories. Something is needed to respond assert sovereignty over the area. A potential issue in theory of purchasing the F35s is a strategic one of maintaining those water rights if in the moment Russia starts moving in suddenly the planes don't work or need parts and the US suddenly has a great point leverage.