How to realize direct arrows with PlantUML?

you cannot have several flows starting from an action nor several flows going to an action

for the UML point of view so you need to add :

1. a decision node after the action "to solve" to have your two flows, each with a guard

2. a decision node after the action "erledigt" to have your two flows, each with a guard

3. a merge node before the action "to solve" to receive the flows from the decision node "check successful" and the action "erledigt".

For (1) use a "if-else" or a "split" in PlantUML

start

:new - please check;

while (check sucessful?) is (is an error)
  :to solve;
  if (duration) then (long)
    :in progress;
  else (immediat)
  endif
  :solved;
endwhile (not an error)

:erledigt;
note left
    reason:
     * done
     * not an error
     * not fixable
end note
stop

@enduml

For (3) may be you can use a "repeat while" also managing (2), but not sure you can in PlantUML without duplicating the three actions (to solve - in progress - solved) or doing them in an other activity you call. In PlantUML the code is drawn from control-structure except "goto", that allows to not cross lines, but you need a "goto" crossing lines. Note there is no problem going to the decision "check sucessfull" rather than to the action "to solve"