From Buddhist perspective, the key ideas of Advaita Vedanta are pretty similar to (Mahayana) Buddhism except the parts where it says that consciousness is everything and that our true nature is consciousness.
Instead we say that consciousness is just one of the phenomena, albeit a very important one. We also say that identifying with anything (including consciousness) leads to suffering, because it makes you vulnerable to change (of that).
What is the view of Buddhism on time and space does it exist?? In Advaita they say time and space do not exist at all.
I mean, obviously time exists in some sense. It's 4:27pm when I write this. I'm not making this up, really ;) Similarly, space exists in some sense. My cubicle at work has very little space. So in some sense space is real too.
In Buddhism we say, that every thing is valid within its certain context or within its certain frame of reference. But outside of that frame of reference, it makes no sense. So we try not to say "exists" or "does not exist" - we think these categories are naive. Instead we say, "here is the context in which it can be observed, here are the limits of that context, so this is the extent to which it can be said to exist".
Advaita says that there is only the universal consciousness and all the objects and people are illusions what is the Buddhist view here?
Well, in Buddhism we agree that everything is connected, or interrelated. Things influence each other and our consciousness arises based on those interactions. But we don't say it's "one" or "many" - because again that depends on perspective. In one sense its one, in another sense its many. We don't want to make one-sided statements.
In (Mahayana) Buddhism we say that separate objects and people are illusion, and that instead it's an interconnected network. We also say that the way things look to us is "like an illusion" because what we see is the models our mind builds, not the actual things. These models can be approximate or completely wrong, but that's what we see. In this sense too, objects and people as they appear to us are illusions.
Advaita says that in deep sleep consciousness do not stop what is the Buddhist view here?
There are different levels of mind, some more coarse and some more subtle. There is a kind of mind that does not stop in deep sleep and there is a kind of mind that does not stop with death.
In Advaita in order to experience our true nature we have to relax our attention from objects and let consciousness be aware of itself. What is the Buddhist view here does Buddhism say that consciousness being aware of itself is our true nature if not how do we experience our true nature similarly to the way advaita vedanta showed us to do and how do Buddhist explain that experience of our true nature.
There are many "schools" in Buddhism that teach different styles, created by different temperaments of teachers and thus better fitting for different temperaments of students. Some teach meditation that is very similar to what you describe, "relax our attention from objects and let consciousness be aware of itself". Others teach different methods. It depends on the student.
In Buddhism we would say that our true nature is "the way things really are" aka "truth" or "suchness". Which is more broad and more correct than "consciousness" because consciousness is just one part of the mix.
Advaita Vedanta says that the world made out of matter in the waking state that we experience is in reality consciousness. They use the analogy of the dream where it seems that matter exists for us in the dream when we wake up we realize everything was consciousness. What is the view of Buddhism here?
In Buddhism we also say that things are nondual - meaning that matter, energy, information and mind are different aspects of same stuff, that it is not fundamentally two or three or four different things. So, when you understand that matter, energy, information, and mind are different aspects of same stuff, you wake up from the dream that coarse phenomena are important, and realize that in fact subtle influences are much more important.
What is the difference between the nature of Brahman and Nirvana? What is the difference between Nirvana and Samsara I read that they are the same? Which implies that Buddhism agree with advaita vedanta that we are in fact our true nature all the time and we have are just in a illusion that we are not.
Yes of course. Generally speaking you are right, and Buddhism says the same. But it is important to really understand this in-depth, not just repeat someone's words.
Brahman is a fancy word for the Absolute, the totality of everything in space and time. Nirvana is the word for the absolutely perfect peace, freedom, and harmony. This perfect peace or perfect harmony is achieved when there is complete integration of all dualities, when there is no more conflict.
In Buddhism we say, it's not enough to just say that everything is already perfect, that universe is in harmony, and that samsara is nirvana. This is true, but not enough. We also say, it's not enough to just sit and let consciousness be aware of itself. Instead, we say, we should work on eliminating the conflict, both in our lives and in our minds. And how do we eliminate conflict?
We don't create outer conflict with our behavior. We create outer harmony with our behavior. We don't create inner conflict with our thinking. We create inner harmony with our thinking. We let go of childish simplifications and attain real understanding. This way we don't just say that everything is Brahman, Nirvana, Harmony and Peace - we actualize it in our life.