I would like to begin with a word of caution.  These answers were given to specific individuals under specific circumstances.  The answers provided may not be appropriate for everyone.  Also, these answers are limited by the level of understanding I possessed at the time they were offered.  Keep this in mind; use what is beneficial and disregard what is not.

How is this Yoga different from others?

Answer:  Typically, Yoga is taught as a series of willful techniques.  The guru provides instructions, and the student follows to the best of their ability.  As the sadhaka progresses, corrections are made, techniques are modified, and new teachings are given.  

No doubt the above path works, but there are some inherent difficulties.  The first being finding an experienced teacher, but even if you do find a genuine teacher, their methods may not be the most suitable for you.  Even if you find the right method, how long should you practice, to what degree or intensity, and when should you move on to a different technique?  A teacher can assist with all these questions, but what happens after the teacher passes away?  These problems are natural, and they can all be worked through, but there is another way that eases the difficulty. 

In the tradition I belong to, the Guru awakens the prana shakti through a look, touch, or mantra (or a combination of them).  Once the prana shakti is awakened, the sadhaka surrenders it to God in meditation.  Everything that follows is spontaneous.  All asanas, pranayamas, mudras, bandhas, etc happen without the willful effort of the sadhaka.  Whatever is required for progress happens happens naturally, in the correct sequence, and to appropriate degree.   

What you’re describing with the kriyas I interpret as massive amounts of purification taking place.  Is that correct?

Answer: The purpose of kriyas is purification.  What is described as being purified varies between teachers.  Some say sanchit karma, some say prana, some say the mind, and all are correct. 

I'm curious, are you sympathetic to the teachers/teachings that say all of the purification is not needed?

Answer: Whatever is true is true right now.  Nothing new is gained with realization, but something is lost.  To realize what is true in this moment, limiting beliefs and false concepts have to be discarded.  Meditation is one tool used to purify the mind enough so that a breakthrough can occur.  Even more importantly is the purification that is needed to abide as the truth.  The classic yogic texts all echo the same idea, both jnana and yoga are required for moksha.  Even Sri Shankaracharya said that if you cannot grasp Vedanta then more Hatha is required.  

The gradual vs sudden enlightenment argument is a very old one, and both sides are true from a perspective.  I say get it if you can get it.  If you can't get it right away, then keep trying.  

What should I do when the kriyas become too intense?

Answer: There are a few things I can suggest for now.  If you are uncomfortable with the kriyas (spontaneous movements) that are happening, and you find yourself unable to surrender them to God (whatever that might mean to you), then you should (1) reduce the amount of time devoted to meditation for the time being, and (2) increase your devotional practices, and possibly (3) consume some tamasic food, such as fried vegetables and/or breads.  Dairy can also be helpful.  This will curtail the energy for a time.  Additionally, you can also pray to God (again, whatever that might mean to you) to take the kriya from you until a time when you are better prepared to experience it.

Notice above that I said, "surrender them to God" and not "surrender to the kriyas."  You should only ever surrender to the Absolute.  God knows what is in your best interest and is working toward your benefit.  You can trust this supreme intelligence, but never surrender to any phenomena, which are all really just illusions in reality.

What is the mind and how can it be used in spiritual practice?

Answer: The Western concept of the "mind" and the Eastern concept are not identical, and it creates confusion when the two are conflated.

In the West, we are inclined to think that there is an entity called the mind, and it produces thoughts.  Furthermore, there is no distinction between Consciousness and mind in this model.  

In the Indian traditions, there is chitta, which is Consciousness (Chit in sanskrit) with a limiting adjunct (creates the illusion of many limited Consciousnesses vs one universal Consiousness), and this chitta takes the forms of manas (mind or thoughts), ahamkara (ego or literally, "I-doer"), and buddhi ( the faculty of intellect or reason).  In Patanjali's Yoga Sutras, Yoga is defined as "chitta vritti nirodaha" or "Yoga is the stilling of the waves of the mind stuff."  What is the purpose of calming the waves of the chitta?  The next two verses provide the answer; I'll paraphrase.  "Then, pure Awareness can abide in its true nature.  Otherwise, Awareness takes itself to be the waves."  The stilling of the chitta allows for the opportunity to see who you are when there are no thoughts.  This is called nirvikalpa samadhi in sanskrit.  It is samadhi (or meditative absorption) without thoughts.  It would be easy to believe this is the pinnacle of spiritual achievement, but that would be a mistake.  Once nirvikalpa samadhi is achieved, then thoughts need to reemerge and be transformed into sarvikalpa samadhi, or samadhi with thoughts.  What was experienced without thoughts must be reflected in thoughts; there must be a "Brahmaakara vritti" or a thought that is absolutely clear and certain that you are that singular, unlimited Consciousness that has produced the illusion of an individual and world.  The problems of bondage and suffering are in the mind, and they must ultimately be resolved in the mind.  In reality there are no problems at all.

Now, the individual cannot accomplish the above (stilling the waves), since the individual (ahamkara) is itself a wave.  Let me repeat, a wave cannot still a wave.  To enter nirvakalpa samadhi, the individual must be dissolved.  There is nothing "you" can do to enter that state.  Every technique is performed by a doer, but it will only take you so far.  There must be a Guru or a God(dess) that ferries you there.  The only thing you can do is surrender. 

What is meditation?

Answer: Meditation is both a state and the process used to arrive at that state.  The meditation state is the steady flow of attention to one thing.  That one thing can be large or small, subtle or gross.  It can literally be everything in awareness or limited to just the breath. 

The process of noticing your attention wandering and bringing it back to your object is called concentration.  When the attention is able to remain on the object uninterrupted, it is meditation.  When meditation is sustained until the duality of subject and object dissolve, it is samadhi.

Is a guru necessary?  In this age, can't I learn everything online?

Answer: It's unfortunate that the guru/disciple relationship has been demonized in the West, even if it is understandable.  A living teacher is indispensable for most seekers. 

Almost every other endeavor in human life necessitates a teacher, but somehow we foolishly believe we can figure out spirituality alone.  It's not impossible, but unlikely.   Try learning quantum physics or neurosurgery by watching YouTube or shopping on Amazon.  Can you imagine how disastrous the results would be? 

Finding a qualified teacher can be challenging, but it will be worth the effort.  If you cannot find a living guru, then it has been suggested to take Lord Datta as your guru.

In Vedanta there an emphasis on knowledge as opposed to mystical experiences.  Which is correct?

Answer: The scriptures have declared that both Yoga and Jnana are necessary for moksha.  In the beginning, Yoga is the emphasis and Jnana plays a lesser role, later Jnana becomes the emphasis and Yoga plays a lesser role.  Some schools of Vedanta focus on the later, since they assume you have already completed a high degree of Yoga sadhana, either in this life or a previous life.  This is not true of all schools of Vedanta.  I was a student of Sri Ramakant Maharaj, and he emphasized the importance of both Dhyana and Jnana.  He repeatedly said that meditation was necessary to absorb the knowledge given in satsang.  Without meditation, the mind will reject the truth. 

Is the "experience" of the Sahaja state a mystical experience or is it "that which pervades all experiences"?    

Answer: It is both.  As you said, the Sahaja state is always present, but until the mind is purified, it can be difficult to recognize.  The advanced meditative states can allow us to see our natural state more clearly; after which, it will be easier to identify it in all states.  Knowledge of the Self is still necessary as well.  Without that, even if we have a clear vision of that natural state, we may not recognize it for what it truly is.