Seems reasonable

Until recently, I'd have said that I trust the voters to sort out who is better qualified and generally, they've rejected candidates who don't present a plausible enough C.V.

And while I'm very unhappy with the results of the 2016 Presidential election, I'm not sure that it demonstrates that the voters are reliably unable to figure these things out. Trump's bizarre win over Clinton was the product of a whole lot of things, not just that he's a skilled bullshitter.

The bar could be raised higher or at least there could be the establishment of certain conditions for election to public office. For example, in nearly every company employees undergo an annual assessment in which their performance in the past year is reviewed. If the review is favorable then the employee is usually given a pay rise and or a promotion.
Why should politicians be exempt from annual or end of term reviews? Criteria can be set up whereby their performance is measured in terms of a percentage of promises and pledges that they kept with regard to their electoral mandate. Not to be too harsh in setting such criteria we might say that if they have kept 50% of their promises and pledges then they are eligible for re-election to public office.

I think that a government should be guided by the scientific method... Anything that does not work should be removed from government and a theory should be written on the things that work

You would certainly expect a person who is going to practice medicine to have the relevant experience. However, when it comes to politics I am reminded of a statement made by one of your fellow countrymen, Dr. Thomas Szasz who said: "Politics is the art of making lies sound truthful and murder respectable." That being the case and or criteria for public office then I am inclined think that there are indeed many who meet the requirements.

It depends on their role. If they're a standard Member of Parliament (or a state representative or whatever) then being voted in by the public is all that counts. However, if they're going to take on some greater governmental role, for example Chancellor of the Exchequer (I don't know what that role is called in other countries), then some sort of expertise in a relevant subject would be desirable.

Someone like Obama ????

Yes,both political education and experience

Yes

No. No matter how bleak it is now, there should be no licensing of politicians