Medieval times - Was the royal throne always given to the 1st born son? If so why?

Often, but it did ultimately depend on the law or practice of the country concerned. Sometimes the monarch had a role in nominated his own successor - e.g. he could nominate one of his sons, but not necessarily the eldest. Sometimes the successor was chosen from among the previous king's family. But over time more and more countries gravitated to the "eldest son" rule; it made for greater certainty and fewer disputes over succession.