Why is Vaisakhi a time when Sikhs like to join the order of the Khalsa?
It is the anniversary of Guru Gobind Singh initiating the first five people into the Khalsa, so it is an appropriate time for Sikhs to follow their example and join the Sikh community.
Was there any other outward sign that the Khalsa Sikhs took on apart from adopting the Five Ks?
The men took on a common surname, Singh ('Lion'), a reminder to be courageous, which they still do to this day. Women take on the name Kaur ('Princess'), to emphasise dignity. It was then that the men started to wear turbans.