Questions about time and space (from beginner) To be honest my knowledge about astronomy and related physics is close to zero. However, since I studied math a bit, I would like to ask a couple maybe stupid questions, which I am curious about and I don't know who and where to ask.

A) Projection of life

Premises:

As Carl Sagan explained in his "flatlanders" story, we can imagine high-dimension space by making projections into space with lower dimension. 
As we learned at elementary school time is the fourth dimension.

Question:

Is it right that what we see/feel in every moment is projection of some 4D reality into our 3D world noticed by our senses. 
For example, If my eyes were able to "somehow" see in 4D and I pointed my eyes to a person, would I see that person in all stages of his/her life from birth to death as a single "entity"? In every second we are only a projection of our 4D representation to our 3D world? 

B) Parallel realities

Premises:   

If we imagine 1D space as a line without ends, 2D space as an unbounded plane and 3D space as an unbounded space, then I could put infinity number of parallel lines into 2D space and infinity number of parallel planes to the 3D space.

I have read that there are at least 10 dimensions.

Questions:

Can I put infinite number of 3D spaces into a single 4D space? If yes, then if we for example chose geographic coordinates of Earth-Italy-Caesena as place and 49 B.C. as time coordinate, we would be probably close to event when Caesar screamed his famous: "alea iacta est". 

If we considered that 5th dimension exists and that we could put infinite number of 4D spaces into 5D space, then we would end up with infinite number of parallel realities, in which Caesar did not crossed Rubicon, or did not even exist. Is it right or complete nonsense? Can be somehow proved that this is right/nonsense?
A)


  Is it right that what we see/feel in every moment is projection of
  some 4D reality into our 3D world noticed by our senses.


It's more similar to a slice, hyperplane or hypermanifold, less to a projection.


  If my eyes were able to "somehow" see in 4D and I pointed my eyes to a
  person, would I see that person in all stages of his/her life from
  birth to death as a single "entity"?


In a classical world, yes.

B)


  Can I put infinite number of 3D spaces into a single 4D space?


Yes, a possible mathematical description of such a space-time is a 3+1-Minkowski space-time.


  If we considered that 5th dimension exists and that we could put
  infinite number of 4D spaces into 5D space, then we would end up with
  infinite number of parallel realities, in which Caesar did not crossed
  Rubicon, or did not even exist. Is it right or complete nonsense? Can
  be somehow proved that this is right/nonsense?


That's close to the many-world interpretation of quantum theory.
But it's thought of as an infinite-dimensional Hilbert space, as one of the simpler ways of thinking.

Thinking of a 5D space-time as a collection of all possible 4D space-times is less suitable, since it would be a mere set of 4D space-times without meaningful structure. Take Ceasar crossing Rubikon a day earlier or day later or a meter to the left or a meter to the right with or without a leaf falling from a tree, or a huge number of other versions. Which would be the correct order to pile up these versions to a 5D world? The infinite-dimensional Hilbert space model solves this ambiguity, and provides a meaningful metric for the set of all possible worlds.

The 10-dimensional models of some string theories are something else: The 6 extra-dimensions are thought to be curled up, and tiny.

We have no access to parallel worlds, so it cannot be proven by observational evidence. It's a mathematical model. It's possible to prove theorems within the mathematical theory, but that's usually based on axioms, or assumptions. Mathematical theories may, but don't need to match with observation, depending on how the axioms match to physical "reality".