Should "The tour lasts almost four hours" be accepted? In English I would say the meaning is almost exactly the same, except that 'almost' may imply that it lasts just short of four hours, specifically.
Yes, if you use almost, that implies that the trip lasts for less than four hours. If you use about or approximetly, however, it could be three hours and fifty-eight minutes or four hours and seven minutes.
You changed verb and subject. The German sentence is about "die Tour" 'doing something'. Your sentence is about the duration of the tour. The transported meaning is okay but it's definitely no translation for the German sentence given here.