Learning about different problem solving strategies and when to use them will give you a good start. Problem solving is a process. Most strategies provide steps that help you identify the problem and choose the best solution. There are two basic types of strategies: algorithmic and heuristic.
It should be 'No vacancies' (plural). Vacant means empty/free. Vacancy is the state of being empty, therefore 'no vacancies' = no empty rooms.
The vacancy announcement must contain a statement that the possibility exists for extending the time-limited promotion in increments of one year, up to not more than five years, and/or may be made permanent without further competition when it is expected that the position may be extended or made permanent.