As to why every generation thinks it's the end of the world, well,... um... Ya got Me by the sneakers! Got any theories on that yourself?

Your next question has more to do with Cosmology than straight physics. But, Astrophysicists join in significantly also at different places to speak to the particular physics of it all.

To my understanding, a closed universe would be sort of like the "closed" area of the surface of a sphere - the surface would be curved into itself and physically finite. If you travel in a straight line on the surface of a sphere, you ultimately end up back where you started - there is only soooo much space (surface area in this case) on the sphere, even if it keeps expanding like a balloon getting inflated.

An "open" universe would be one in which you could travel forever and not reach any end or limitation.

So "open" and "closed" refer to the topology of space (more correctly spacetime) - just like the surface of a sphere is a curved topology (as opposed to flat), spacetime can have a topology too.

The Big Bang theory is a result of observing that our universe is expanding - in general terms (there are specific exceptions), galaxies are all moving away from each other. If you mark dots all over a balloon, you'll see that they all move away from each other as the balloon inflates. And, the greater the distance between any two dots, the faster they move away from each other as the surface of the balloon expands. So, our universe is expanding because space itself is expanding. Yes, there is such a notion as the "fabric" of spacetime.

So, if things are moving away from each other now, then we can extrapolate backwards and assume that the universe was smaller yesterday than it is today. And that it was smaller the day before yesterday than it was yesterday. And so on, and so forth. Until.... we reach the conclusion that the universe must have started out as a very tiny thing. Indeed all our observations seem to support this theory.

This is all fascinating stuff for me - thanks for the question! I can only hope that I was somewhat accurate in my explanation.

The sphere notion wasn't fully developed in my mind.  I still cannot believe there is not a further space out beyond each subsequent space.  There is a notion also, I have read in passing, that the universe contracts, as well as expands.  I don't know what implications are made from that theorem.  I have some physics books that have gained some popularity in recent years.  I'll have to read more before I comment more on cosmology.  Right now I can't remember the basics of what Hawking wrote on string theory so many years ago.  I have Baby Universes and other essays, so I'll have to skim back over that.

One very key concept to keep in mind is that our Universe is NOT necessarily expanding INTO anything! The space and time of our universe were both created in the Big Bang. Prior to that, there simply was no spacetime.

Another concept to master is the dimensionality involved. Start with imagining a flat surface being stretched. If the universe was only 2 Dimensions, then what we THINK is flat might actually be the surface of a sphere. The Surface of a sphere is two dimensional -curved, but still only 2 dimensions. As the surface of the sphere (or picture a balloon) expands, the surface expands, but it is not expanding INTO anything. Remember though, there's no actual sphere, ONLY the Surface!

Now for 3D. Our own 3D universe may be the surface of a hypersphere (4 space dimensions) that is expanding. Now, that surface (our 3D space) is not expanding INTO anything - there need not be anything beyond that surface.

As to your other concerns, I'm not aware of any theory proposing that our universe contracts. If it is expanding, as the consensus has it, then it cannot also contract - at least not at the same time. Expansion may slow down, stop, and then contract some time in the very distant future if somehow gravity wins out over the theorized "dark energy" which we think is the driving force behind expansion.

Baby universes have to do with the Multiverse cosmology, which proposes that our universe popped into existence within another universe and subsequently detached from that universe and expanded in and of itself in its own right This might be crudely like a bubble forming on another bubble and then splitting off from that original bubble, forever estranged in an irreversible separation. And the multiverse theory also implies baby universes popping out of our own universe.

This can be pretty mind bending stuff! And if you end up understanding it with a minimum of effort, then I will have to start picking Your brain! :-)