-> Anatman, Vacuity, Eternality, nihilism...So much is said, so less understood :/ Between Nihilism (nothing is real, I do not exist) and Eternality (Everything is real, I never ceased to exist) isn't there a clear definition, or at last a middle path ?
Yes, Madhyamaka is the Middle Way.
-> In Sanatana Dharma, it is said that Universe and time have no beginning and no end (multiple cycles of creation, preservation, dissolution etc...) and same is for individual soul.
In Buddhism, since there is no concept of individual soul, what goes from body to body after death ?
The mindstream goes from body to body. The mindstream carries karmic impressions that manifest into a new life. Basically, the mindstream is a collection of seeds that determine what is reborn, where it is reborn, and the manner of its next life. There is no individual soul because an individual is simply a collection of karmic components, all of which are conditioned by other factors and causes, all of which can change, grow, die, increase or decrease. Therefore they come together from numerous factors like molecules are simply combinations of atoms. When you break it down, you can't find any essential, absolute self, just lots of pieces that are always changing and empty of inherent existence. The easiest way to see this is to look at your own life. Who were you when you were 5 years of age? Who are you now? Are they the same person? No, they are not. You are conditioned differently now than you were, you will be conditioned differently 20 years from now. This changing nature of the self implies there is no eternal soul that is always the same, rather there is a collection of many things that come together to make up what we falsely call a "self" but which is ever changing and ultimately insubstantial and unreal, just like every other phenomena in the universe. However intellectually knowing this is only the first step in experiencing real emptiness, which comes about as the result of purifying the minds ignorance, studying, and practicing.
Is it potentiality of Budhahood that we all possess ?
Everyone has Buddha Nature. The path is meant to show a person that nature, how to reach it, and how to remain in it. Buddha Nature is essentially a state of complete selflessness where one is no longer conscious of duality at all.
Is this potentiality of Buddhahood common to all beings (everyone in one common pool) or individual (One drop ofthe pool for everyone) ?
(Of course "potential Buddhahood" is completely free from Ego)
Is the view of eternal, endless, beginless universe okay in Buddhism ?
Ultimately the Buddha called thinking about the beginning and end of the universe an imponderable because our minds can never encompass the answer. Therefore its considered a distraction to our practice, so its best to leave it alone all together. We are here, now, dealing with this present situation. Our situation is dire, and we need to find a way out. The most important thing is to address this situation in the here and now, and not concern ourselves with trying to grasp something that is essentially infinite, a question we can never really answer.
-> In initiation of KalaChakra, there is something that I don't really understand. It talk much about gaining access to our "clear light"
Is it some kind of what others commonly call "Subtle body" ?
The clear light is a term indicating a level of awareness that one can reach after one has sufficiently purified their mind and seen their Buddha Nature. Recognition of the clear light is recognition of ones own Buddha Nature. The clear light is the naturally manifest luminosity and clarity of mind that appears when we properly apprehend emptiness, which is equal to being totally selfless or recognizing our Buddha Nature.
It is not the subtle body.
Is it something that all sentient beings have ?
Is it something present in all the universe, like a stream ?
Because the clear light is more or less synonymous with Buddha Nature, it is within all sentient beings. Because sentient beings are deluded and confused, they are not normally aware of it. Buddha Nature is our individual experience of the universal ground of all being, and therefore in a sense it pervades all things whatsoever, all phenomena, all creatures, and whatsoever appears in all of the universe.
How is the womens situation when they choose to become nuns or renunciate (welcomed or difficulties) ?
There are many places that will accept women as renunciates, nobody in Buddhism has any real problem with women practicing, and in Tibetan Buddhism women have played a very important role in the transmission and preservation of Dharma. As with all human institutions, Buddhism contains men who are averse towards women for various reasons. However, I've seen women I consider to be enlightened beings and see them no different from men. This, in my opinion, is the proper view towards women in Buddhism.
How are the womens renunciates and nun viewed by the different schools ?
As Buddhist practitioners seeking enlightenment.
Does women teachers and lama exist ?
Yep! They are no less enlightened and no less profound than their male counterparts.
What is the view and situation of womens in Buddhism in a broad sense ?
Depends on who you ask. Most Buddhists are welcoming towards women, think highly of women, treasure and value the unique wisdom that women can manifest into the world, and overall see women as equals. There are of course Buddhists that don't feel this way, but in my opinion they need to strengthen their Dharma practice if they are averse or negative towards women.
Is it a problem for a lama male to initiate a female ?
Not at all.
Can Enlightenment be explained, or conceptualized ?
It can be explained and conceptualized, but it can never be understood by explaining or conceptualization alone. Thinking will not lead to enlightenment, only more thoughts. This means that the explanation always falls short of the truth, and so intellectually thinking about enlightenment will never lead to enlightenment. Enlightenment is a state of mind free from concepts, mental constructs, and mental projections. It is free and non-attached to all mental phenomena and all emotional arisings. It is in essence beyond words and beyond description.
Is it an eternal state, or only temporary (that diseappear after rebirth) ?
This depends on the level of enlightenment. There are levels that can regress back into ignorance, at the higher levels one gains supreme confidence and solidarity on the path and at this stage enlightenment is called "irreversible".
Does Buddha teachings, and the goal of Bodhicitta/Awakening, give us the means and powers to help the world and ease the suffering of sentient beings ?
Nothing in the world is more effective than Buddhism to accomplish this goal.
(if yes) Does it give us the mean/power to help the world and ease suffering of sentient beings even between rebirths, or in next rebirths, even if we are beyond Samsara ?
Complete enlightenment gives us the capacity to endlessly help all sentient beings in whatever situation we desire or choose, wherever the need is greatest. It even allows us to enter hell and help the beings there. There is no limit to the capacity of a Buddha to benefit and lead other sentient beings out of samsara.
Does Buddha teach compassion to all beings, for every human and every animal ?
Every being whatsoever, because all beings share the same essential Buddha Nature, even an ant.
I am very sorry if it seems silly or selfish questions _/\_ I am also sorry if my ignorance hurt anyone, I do not mean to hurt anyone or to seek to anger or provoke any problem here
They are neither silly nor selfish, they are all good questions. No harm done.
Since you mentioned Lam Rim, you might consider picking up the three volume translation of "The Great Treatise on the Stages of the Path Towards Enlightenment".