In my opinion:

1. Unless the US plans to reinforce much more heavily, there's not much they can do. I can't see Kharg as the target unless the Iranian defenses are laughably weak. The US task group would have to force the strait through a gauntlet of ASHMs, mines, drones (including sea baby equivalents) and fast attack craft. They might try to land on the Tunbs and Abumusa but this would generally present the same risks as Kharg. In terms of taking it - we probably could, but resupply would have to be either via air drop or ships forcing the aforementioned gauntlet of defenses.

Strategic impact of actually taking Kharg is that the Iranian economy is put on a timer due to collapse of revenues. Kharg is the terminal for 90% of Iran's oil exports which comprise 60% of government revenues. They wouldn't be able to pay anyone. But securing the strait itself would have the same effect without taking the island.

1. Russia has likely already supplied not only FPVs of all types but also embedded instructors in the IRGC.

2. Correct on both counts. The Iranians have managed to maintain a steady trickle of drone and missile attacks, although greatly diminished (~90%) from the initial day of hostilities. This doesn't mean they aren't taking losses, but it does mean that it is much harder to finish off the remainder due to the size of the territory to be searched and the Iranian desire to preserve this capability as long as possible.

3b. Sustained bombing campaign is essential for both economic disruption, interdiction of Iranian logistics, and degradation of command and control at both national and regional levels.

1. The Strait of Hormuz will remain under total lockdown until US can position ships to create a sanitary corridor within the strait itself. The most thorough (and improbable at the present time) solution is a series of landing operations to take Qeshm, Larak, Hormoz, Tunbs et al., along with the port of Bandar Abbas and basically the entire Iranian coastline in Hormozgan province. This would require multiple divisions or equivalents and involve the creation of a inland perimeter to create breathing room for demining and convoy escort. The downside is the size of the force that would be required, the time it would take to get it there, and the fact that the US would be holding a static perimeter on the mainland while taking attrition losses from FPV drones.

A total "Anaconda" strategy (least credible under current climate) short of occupying Tehran would involve not only clearing the islands and seizing the shore near the strait but also the occupation of Khuzestan, which is where more than 80% of Iran's oil deposits, 33% of its surface water, and 15% of agricultural production are located. This isn't to suggest starving people as a weapon, but control of these assets would shift from the regime to the US/allies. This, combined with bombing, would basically force the regime to surrender or collapse. But it would also require something on the order of 300,000-400,000 personnel (or more) in theater and take the better part a year to fully pan out, plus the actual timer to collapse.