1. Alaska could remain Russian; its not really costing them anything, it was just nice to sell it to make money. When the Klondike gold is discovered Russia won't want to be parting with it.
2. Hawaii could see a more assured succession leading to a longer view being taken. Britain could easily have taken it as a protectorate, and ironically if Russia retains Alaska it is going to be MORE in Britain's interests to intervene in Hawaii, since the Russians have big interests there to. So 1. actually pretty much leads to 2. here
3. Greenland, its not exactly vital to Danish interests or its economy, its getting over the issue of pride that would be the problem. Offer enough money at the right time and it seems possible. When the right time is, is the question. But a note would be that 1. and 2. above would lead to a USA taking a more EASTERN approach (ie its East)
4. "The Caribbean" is just not homogeneous and can't be treated as a whole. It consists of independent nations and the colonies of Spain, France, Britain, the Netherlands, Denmark and (until the 1870s) Sweden.
What the USA could do is build up formal protectorates on the basis of the European powers, whilst the long periods of civil war in Cuba could be the basis for intervention earlier, even war with Spain if the US had a navy capable of sustaining this.
Spain though is not an isolated country, and whilst before the 1890s the USA could, by building modern warships instead of crappy monitors, have mounted a challenge to it, it could not if Spain was supported by any other European power