In a normal parliamentary election, how does a voter vote for the candidate he wants to be the Prime Minister if that's possible? Is it a direct vote. Or, do you have to vote for a Minister of Parliament who says they'll vote to elect the PM you favor? Another way?
From the UK.
In a normal general election a vote is held across the UK on one day. The country is divided into constituencies and each has a member of Parliament (MP). Most candidates stand representing a political party although it is possible to stand for election as an independent. Often there will be 4 or more candidates. The one who gets more votes than any other candidate in the constituency is elected as a member of the House of Commons (the other house is the House of Lords, members of which are mainly appointed for service). Each political party taking part has a leader, usually elected by the party public membership. Each party also has a manfesto of what it would do if in Government.
The party that wins the most seats in the House of Commons forms the Government and the leader appoints department ministers, e.g. Chancellor of the Exchequer (Finance and Taxation), Foreign Affairs, Home Secretary (UK internal), Defence, Education, Culture and Sport, etc, etc. If no one party gets an overall majority (>50% of the members) then it either forms a minority government (difficult to operate) or forms a coalition with another party to ensure that between them they have >50% of members.
At any time a vote of confidence can be called in Parliament and if lost there is a general election. If a party's MPs get fed up with its leader it can make life very difficult for the leader as has just happened in the UK. As the leader is elected by their party, the party MPs and members in the public can elect a new leader. If that new leader departs much from the manifesto on which they were elected, then a vote of confidence can result.
In the UK this is regarded as democratic, though some want constituencies to have constituency proportional representation rather than first past the post.
That is how I understand it, and it is the sum of my knowledge - please don't ask me any questions.
Jonathan