What is Shani's vakra Drishti? Is it bad or good? What are its consequences? Is there any role of karma to remove vakra Drishti if one is likely to have? What should one do or don't do if one is having that?
A brief reference is made to the question. As far as the effects of Vakri grahas go I have not given any answer.For the last part of the question a detailed response is given. the answer may not be complete in all aspects.
In Hindu astrology, Vakri grahas are those planets of the Solar System other than the Sun and the Moon that appear to move backwards, which apparent motion is due to earth’s orbit. Vakri in Sanskrit means twisted or crooked; it also means indirect, evasive and ambiguous. A Vakri graha is also known as the Saktha graha. Vakragati confers exceptional i.e. Cheshtabala, to Vakra grahas whose strong influence is expressed by the manner they affect the Natal Chart and by their transits. The two Lunar Nodes have perpetual retrograde motion.
Shani's vakra drishti can be removed in a number of ways. I have forgotten the name of the exact source, but I have the words.
After completing his education, Lord Hanuman wants to repay his guru Lord Surya. Though Surya tells Hanuman to go back without repaying him anything, Hanuman insists him to ask for his guru dakshina. This is the time when Lord Surya talks about his son Shani who never listens to him and creates problem for everyone. He asks Hanuman if he can make him mend his ways.
Hanuman then enters Shani Lok and request Shani to return to his father. Shani who is too haughty cannot believe the fact that Hanuman could enter his Shani Lok effortlessly. So, he decides to teach Hanuman a lesson. He then climbs on Lord Hanuman’ shoulder and implies all his energy to put an influence on him. However, much to his surprise, it doesn’t affect Lord Hauman in any way.
In fact, Lord Hanuman increases his size so much that poor Shani is caught between the ceiling of the room and Hanuman’s shoulder. Now that the pain becomes unbearable, Shani requests Hanuman to leave him with a promise that he would never trouble anybody who is a Hanuman devotee, moderating all his effects in front of a Hanuman devotee. Hearing this, Hanuman released Shani Dev from his catch.
Next, Shani dev asks Lord Hanuman for til and tail so that he could apply on him, and get away from the pain. Ever since then it is a normal practice to offer oil and black til in the name of Shani Devta. It not only soothes his pain, but also makes him beneficent towards Ram and Hanuman devotees. This is the reason why every Saturday you see a huge line in every Hanuman temple to visit both Hanuman and Shani devta. People who give an offering of til and tail (oil) to Shani devta on this day are not affected by Shani’s dosha.
In another story, the boon of Lord Shiva and Brahma made Ravana invincible. > He wanted a similar fate for his son Meghnath, and so when he was about to be born, Ravana kidnapped all the 9 planets and placed them in the 11th position so that his newborn too could be immortal and invincible. This made him lock up all the planets including the Saturn,that is Shani Dev in a place where it would be very difficult for them to get out.
However, Lord Hanuman reached the place when he was searching for Maata Sita in Lanka after she was kidnapped by Ravana. It was then Lord Hanuman rescued Shani Dev from Ravana. As a thank you gesture, Shani Dev gave a boon to Lord Hanuman that the effect of Shani’s inauspiciousness will never affect him in any way. In return, Lord Hanuman mentioned that none of his devotees should be affected as well. Shani dev obliged. This is the reason why people worship Shani Dev on Saturday and why Shani do not cause adversities to Hanuman devotees.