Can a person learn Jnana Kanda of Vedas without learning the Karma Kanda? Is there any rule like one should learn the Samhithas and Brahmanas first, then only he can proceed to Jnana kanda?
No, normally one can not. Because, one needs the 'Sadhana-Chastustaya (Fourfold Requirement)' to learn the Upanishads. These four are:
nitya-anitya-vastu-vivekaha ihAmutra-fala-bhoga-virAgah-samAdi-shat-sampattih mumukshutvAni (VedantasArah 15)
Meaning : These fourfold requirement are Nita-Anitya-vastu-viveka (1), iha-amutra-fala-bhoga-viraga (2), samadi-shat-sampatti (3) and mumukshutva (4)
The first word means the comprehension that everything is transient, and only Brahman is eternal. The second word means complete dispassion for all th pleasures in either this world or in the other worlds (heavens or different abodes of forms of God). The third word means the complete control over the mind and the senses so that they can be withdrawn instantly from the material objects, no further passion for any worldly object, perfect perseverance, perfect stillness of mind (samadhi) and firm faith on the words of the Acharya and the scriptures. (VedAnta-sArah 16-24).
It is clear from the above that no ordinary person is entitled to study the Vedanta. The aspirant therefore must practice the Karma-kanda prescribed by the shastras ie the 'Nitya-Naimittika-KAmya-karma'-s, prayaschitta and Upasana (worship of God).These has been mentioned as essential to obtain the competence to learn the Upanishads (VedAntasArah 6-13).
The Viveka-Chudamani also writes:
sAnsArika-sukhAsaktam brahmajno'smiti vAdinam/ karma-brahma-ubhaya-bhrastam tam tyajed antyajam yathA//
English Translation: That person should be rejected as an outcaste,who has passion for sensual enjoyment and says that 'I know the Brahman', as that person is fallen from both Karma amd Brahman(Jnana).
For this reason, Swami Vivekananda or other direct disciples of Sri Ramakrishna did not encourage the common men to follow the Jnana-marga. Swamiji writes:
All people cannot take up this Advaita philosophy; it is hard. First of all, it is very hard to understand it intellectually. It requires the sharpest of intellects, a bold understanding. Secondly, it does not suit the vast majority of people.
Swamiji inspired the masses by preachings the message of fearlessness (Abhih) of the Upanishads and the grand tattva of Atman or Brahman, but He emphasised on the combination of all the four yogas ie Karma-yoga, Bhakti-yoga,Raja-Yoga and Jnana-Yoga. He never asked the ordinary or common people to follow the Jnana-marga alone as He was well aware of its fruitlessness and dangers.