a) Inheritance is a problem because instead of property going back onto the market it is instead like you say kept inside families and typically used as investment properties.

b) Immigration isn't keeping salaries low. Companies are. Because they have eliminated unionisation and so workers have no means to demand for higher wages. And with so much remote talent companies always have a backup plan in case there is a supply shortage.

c) As you say they compete for the same resources. Now why can't there be more homes ? Because older people fight increasing density, refuse to support taxes on investment properties and are increasingly refusing to downsize once their children move out. Remember for many their legacy depends on high property prices.