Republican candidates are nominated by the most influential members of the party.
Then candidates are elected.
I don't think so. I think you have the terms reversed.
A candidate is anyone who runs for his or her party's nomination, and the nominee is the candidate who the party's nominating convention chooses to run for the office in the general election. That's why it's called a nominating convention.
Delegates to the nominating convention may or may not be the "most influential members of the party", but in either case they are still either elected by Republican voters in primaries or chosen by a caucus composed of party members.
I think your description is how it is supposed to work, and Designer's is how it actually happens, because of a lack of understanding and participation on the part of the American people.