First of all let me note, that the word "consider" isn't translated as "считать" in this context. The right translation here is "рассматривать, обсуждать, обдумывать".
Now considering your questions:
1. "Представлять собой" means "to represent".
2. "Решение" means "solution". You know there are such people who are called architects. Their job is to think out, to contrive a design of a building or an architectural place of some kind. So they thought and thought and thought and after that took pencils and draw some drafts, sketches, drawings and all this is called "architectural solution".
3. The word "третий" is written with "и", not "ы". If the author had used the word "который" that would have meant that the Cyprus stone itself made the solution the unique one, if the author had used the word "которое" that would have meant that the solution to use that stone is important, but the word "которое" also implies a choice between several options. So if you use the word "которое" you have to say something about the alternatives. The word "что" doesn't imply the existence of alternatives and it doesn't refer to an exact word in the preceding clause as "который" does. It refers to the whole clause, it has no gender, no case, it's short and simple. Why not use it?
4. "Почему единственный требует творительнымого падежома?"
Because if you put it in any other case, it will be either senseless or grammatically incorrect.
5. The word "пятый" is written with "ы", not "и". The expression "в своем роде" usually translates as "in one's (own) way".