The definition of populism is very simple: telling the public at large whatever it wants to hear at any given time, without much regard to any consistent ideology. To an even bigger extent than mainstream politicians already do. There are populist politicians everywhere, but in the US system it's not really possible to have entire populist parties - each party also must have almost by definition a group of politicians who actually get things done and hammer out policies with difficult compromises, and another group which sets the ideological lines and ensures they are at least somewhat adhered to. In Europe there are plenty of parties which are populist as a general policy, with at best lip service paid to the notion of serious, consistent ideology and policies.
The UKIP used to be a single issue party, with the single issue being the exit from the EU. Before long, they naturally segued into the complaints about too many foreigners coming to the UK, though to their credit they made sure that at least in their leadership there was always a clear stance against racism - Farage has refused to join forces in the European Parliament with nastier parties, even big ones like the Front National. It doesn't take a genius to see that the slow death of the openly racist British National Party is largely if not entirely due to the UKIP sucking them dry, though.
And now in the last year or two, they are trying to branch out and build policies on other topics too. But still, it's obvious that those are the two points that define the party.
Sure, but don't expect them to present anything remotely like a credible budget. Which is not to say the main parties don't engage in a little fantasy here and there, but they are rather more closely watched.
Do read e.g. this. This is literally the first hit if you enter "UKIP economic policy" on Google. Seems I was a little premature in saying that the UKIP was less inclined than the continental populist-right (a better term than far-right, really) parties to go with whatever economic policy sounds best to the voters at any given time.
Hardly a private system. The NHS is sacred in the UK.
In many ways a carbon copy of Alex Salmond's stance: if you tell yourself and your neighbours loudly enough that you really will be better off by leaving the union, it doesn't matter what the facts are. By the time people will face reality, it's too late to go back. The British businessmen, much like the Scottish ones, are not quite so eager to gamble.
In fairness, this is no different from what the Euro-sceptic wing of the Tories has been doing for decades. But again, that's the difference between a governing party and a populist one: in the UKIP, leadership doesn't need to worry about doing the responsible thing, they have the same luxury the Tory backbenchers have.
Because US Republicans actually (and generally quite vehemently) believe that their economic policy is the right one, and aren't generally inclined to ditch it at the first sign of shifting public opinion. On immigration there is more populism in the Republican Party (I remember several elections ago, this guy Tom Tancredo - he seems like a perfect fit for the UKIP), but as I said, it's never the whole party acting like that, there are always the more responsible members looking for a real solution also.
Gay marriage is another good example - why does the UKIP advocate drawing the line at civil unions? Because the Tories abandoned that stance, and left it open for the first claimant to take - most Britons have no problem with same sex marriage, which is why the Tories decided to embrace it (that, and it was a useful proxy for their general message that they had modernized and changed), but there's still some votes to be had in opposing it. Though they then managed to state in an interview that if granted power they would not overturn same-sex marriage, before subsequently denying that - a classic way of letting voters believe that whichever stance they like best is the real one.