What Sadhana or karmas did Swami Vivekananda do?
This answer said he chanted Pranava regularly.
Did he do anything else?
Swami Vivekananda was an incarnation of Sri Vireswara Shiva. He used to medidate from His early childhood becoming still like a rock. He saw divine light everyday between two eye-brows while going to sleep everyday.He worshipped idol of Rama and sita and later of Shiva regularly in His childhood and meditation was his regular practice in His entire life.
Sri Ramakrishna ordered Him to medidate on the image of Maa Kali. He had different visions of Maa Kali, and different mantras.Sri Ramakrishna also taught Him and Him alone Advaitavaada nd asked Him to read the Astavakra-Samhita regularly.Sri Ramakrishna's mere touch gave Him the Highest Advaita experience. In Kashipur, Swamiji experienced Nirvikalpa Samadhi at an age of twentythree and composed a famous song (Naahi Surya naahi jyoti) on His direct experience of the samadhi.Sri Ramakrishna initiated Him by Sri Rama mantra also.
After Sri Ramakrishna left His body, Swamiji and His brother disciples started practising meditation, japa and worship at the Baranagar Math with unimaginable austerity. After some months, Swamiji left for pilgrimmage. He got the grace of Pavhari Baba at Gajipur and of Sri Sri Radharani in Sri Vrindavan.He again experienced samadhi at Hrishikesh and came to know that He was ordained to do some divine works.
He went to the West after getting direct orders from Sri Ramakrishna and Maa Sarada Devi. He always remained in a state that is far above the imagination of any normal individual.He worked tirelessly for four years in the West being established at the top of the spiritual state and experienced samadhi many many times.
Returning to India, He visited Sri Amarnath and Maa Ksheerbhavani temples and got direct vision and boon of Ichchhamrityu from Lord Shiva. He herad the Voice of Maa Bhavani saying to Him.
So He did not need any sadhana.He medidated because that became His very nature: He was spirituality personified. With the same devotion He did the seva of the Nara-Narayanas. He saw God in each and everything and this was forecasted by Sri Ramakrishna long ago.
Actually He came to give us light. The severe sadhana and austerity that He did and practised was for Lokashiksha. He was an incarnation and did not need any sadhana at all for His own emancipation.
(Reference:1. Yuganayak Vivekananda, Swami Gambhirananda, (Volumes 1 and 2). 2.Sri Sri Ramakrishna-Leelaprasanga, Swami Saradananda, (Vol 1 and 2), 3.Sri Ramakrishner Antyaleela,mSwami Prabhananda(vol 1 and 2) 4. Patravali by Swami Vivekananda, 5.Smritir Aloy Swamiji and SmritirvAloy Swami Vivekananda(both published by Udbodhan, the latter having reminisences of many North and South Indian and Western disciples).