Not completely right. The Bundespräsident is elected by the
Bundesversammlung.
You are right with your assertion that the president has (nearly) no political power. The German equivalent to the American president would be the Chancellor.
The Chancellor is elected by the Bundestag, the lower house of parliament in Germany. The parties will tell before the general election whom they will nominate as candidate for that job, the voters do not have a direct influence on that (they have an indirect influence because the parties will more or less listen to opinion polls before they nominate their candidates). So, we do not only have no primaries in the American sense, we do not have primaries at all.