First of all one has to legally obtain the mantra through initiation (Diksha). This is the first step. Next, Purascharan, as prescribed, has to be done.
Without Purascharana, a mantra is stated to be devoid of any powers.
The Puras’charanam of Gâyatrî is repeating this twenty four lakh times
(i.e., as many lakh times as there are syllables in the ...
Yes, except the mantras like "Hare Rama, Hare Krishna" or "Om Namo Narayana" given by saints like Chaitnaya Mahaprabhu, Ramanujacharya to entire mankind, all other mantras need initiation, even if they are simple Gayatri Mantra or "Om".
D: “Can anyone get any benefit by repeating sacred syllables (mantras)
picked up casually?
The word mantra in Sanskrit means ‘that which protects by being meditated upon’ (mananAt trAyate iti mantrah).
Mantra can contain bijAksharAs and name of the deity.
Example: chAmundA mantra ॐ ऐं ह्रीं क्लीं चामुण्डायै विच्चे।
Ganapati mantra : ॐ Gam Ganapataye Namaha
or may contain words like gAyatri mantra:
ॐ भूर् भुवः स्वः ।
According to Yoga Sutras of Patanjali, various Siddhis can be achieved by making Samyama (संयम) on subtle things or quantities. First of all let's clear what is called Samyama:
(Quoting from Swami Vivekanada's Rajayoga: Patanjali's Yoga Aphorisms : Chapter III - Powers)
The combination of Dharana, Dhyana and Samadhi is called Samyama:
त्रयमेकत्र संयमः ...