I found this forum while I was trying to find answers to certain questions that are related to yoga and Kriya Yoga specifically.
I am a probably good candidate to answer your questions, as I have been initiated in the tradition of Kriya Yoga and a tradition related to it, Tantra yoga.
The above claims - as well as many others listed on the SRF website - are very strong claims and many of them are contradictory to one another. These claims also imply their scientific validity as they are called “definite scientific techniques” and the “scientific methods of yoga” in attaining direct personal experience and unity with God.
These claims are not unique to SRF, in fact pretty much any organization that teaches Yoga claims that their techniques are scientific. The claims that Yoga is scientific is also made by the tradition itself from which it originates and by several modern scientists. Why? Where there is smoke, there is fire. Yoga is called scientific because the techniques when practiced as prescribed tend to produce similar effects on the body and mind. This is why they have become the subject of study of many scientific studies and even recommended by prominent scientists and doctors.
Another reason Yoga is called scientific is because like any science it has an epistemology and a systematic theory underpinning it i.e., it is based on a system of thought based on actual evidence. This sets it apart from a faith, because faith is based on belief alone. I will not go into details about the epistemology and scientific theory of Yoga, because I don’t have time.
- How can Yogananda and his followers scientifically prove that someone’s personal experience and the “truths” derived from such experience - either Yogananda’s or that of others - are with objective and scientific validity?
It is proven by gathering data and comparing the data to make generalizations. It is very much like any science, except while most sciences gather external data, in Yoga internal data is gathered. The data Yoga is concerned with is the structures of the mind which are objective, and not the content of the mind, which is subjective. In Yoga psychology for example they have been able to analyze the structures of the mind into a lot of detail, there are about 40 terms in Sanskrit referring to psychological entities e.g., jnanaindryias; the sensory organs from which we receive data from the external world; manas, the aspect of our mind that organizes information from the sensory data received; buddhi, the executive function of our mind that makes decisions based on the data; ahamkara, the ego function which personalizes the data received(i.e filtering it according to personal values, beliefs etc, and chitta, the storehouse of memories of sensory impressions. These are some of the main mental structures recognized in Yoga psychology.
Of course if you analyzed your own mental structures you will find these structures do in fact exist. There are certain predictions I can make about what will take place in your mental world based on the knowledge we have of how these structures work. For example, I predict that if you sit down to meditate by focusing your mind on a focal point. The first thing you will experience is your mind wandering from your focal point into other thought activity. Initially, this thought activity will be high. You will find it close to impossible to hold your mind onto your focal point. If you are able to successfully maintain your focal point for a prolonged duration, I can predict your mental activity will begin to lessen and you will experience the emotional state of calmness. If you can maintain it further, I predict you will experience an altered state of consciousness and altered perceptions of time and space.
The Yoga I have described above is known as the Yoga of mind-control(Raja Yoga) There is another Yoga called the Yoga of body-control(Hatha Yoga) and Kriya Yoga is a type of body-control yoga. Just as we can make generalizations about what will happen in your mental world in meditation, we can make generalizations about what will happen in your mental world when certain aspects of your body are manipulated. For example, if you alter your breathing cycles and reduce your breath from 20 per min to 7 per min, I can predict that your thought activity will lessen and you will experience greater calmness. There are also physiological predictions we can make about what will happen to various physiological indices in your body(e.g., brainwave emission, heart rate, hormone levels) There is ample data if you care to look in peer reviewed scientific journals on this subject.
Kriya Yoga is slightly different to Hatha Yoga, because while Hatha Yoga’s main emphasis is on asanas, mudras, bandhas, shatkarmas to awaken the Kundalini energy in the cerberal-spinal column by purifying the psychic nerves, Kriya Yoga’s focus is on pranayamas to do the same. Kriya Yoga claims itself to be the fastest path to self-realization/god-realization/enlightenment, because it works directly on the energy body(pranamaya kosha) with advanced Yoga practices of breath work and meditation. In contrast, Hatha Yoga works directly on the physical body(annamaya kosha) with lower practices of asanas.
- What kind of scientific proof they can provide that the personal experiences through these yoga and meditation practices are from God, rather than from hallucinations, self-hypnosis, or some other not-shared mental states? (The perceived “beauty” of these personal images, “bliss” or other effects perceived as positive do not necessarily imply the presence of God.)
They cannot provide proof of these claims, because these claims are subjective interpretations of objective mental states. Somebody who is religious minded will interpret these experiences in religious terms like god and heaven etc, whereas the non-religious minded will interpret them in more secular terms like describing feelings(bliss) They are both experiencing the same thing, but they are using different languages to describe it.
- If we assume the existence of God and the spiritual realm, how can they scientifically prove that the experience attained through these methods is from and with God rather than from some other, possibly misleading and malevolent spirits of the spiritual realm?
It is the quality of experience one is having that they can be sure that no evil entity is producing it for them. That bliss that they experience in meditation makes them compassionate, wise and loving people. They return from these states as reborn people. They no longer identify with their former selves. It is like the caterpillar returning as the butterfly. If an evil entity has produced this beauty, virtue and goodness we see in them, then it cannot be evil, otherwise we have a contradiction in terms. If this is evil, then I prefer to be evil 
- Another question beyond the above: In addition to those of Kriya Yoga, do the practitioners and teachers of other forms/types of yoga and/or meditation claim as well that their methods eventually lead to a personal unity with God or this is a special case?
Almost all forms of Yoga make the same claim. Yoga is after all an ancient Hindu science for realizing unity with Brahman(Hindu concept of god) Hence why most Yoga organizations who are loyal to their traditional roots make similar claims.
