Are the theories of Evolution and the Big Bang now binding to Catholics and to be held as true?

I believe the Pope has to speak "ex cathedra" for his statements to be binding. I don't believe Pope Francis was speaking ex cathedra when he was discussing those theories so the short answer would be no, Catholics aren't expected to believe in those things.

There is no official Church teaching on evolution, but this wikipedia article has a very nice summary of the Catholic Church and evolution and provides a history of statements from Church leaders and some theologians. [cf. Catholic Church and evolution | Wikiwand.]

It should be realized that the dedication of a bust is not an occasion where some new Church teaching is going to be given. You go could into how Church teaching comes about. A Pope can speak ex cathedra, but that has only been done twice in history and it is made very clear that he is speaking in this way. For non-dogmatic Church teaching the Pope would issue a document such as an encyclical. If something is going to be required by Catholics then it will be stated in a clear and formal way.

However, this explanation is unnecessary because a careful reading of the statements will show that about the only thing that could be considered as a new teaching would be the idea that the scientific theories of Evolution and the Big Bang do not rule out the idea of creation and can even presuppose the idea of creation.

The Pope does not endorse evolution. He says that evolution does not rule out the idea of creation. "The evolution of nature does not contrast with the notion of creation, as evolution presupposes the creation of beings that evolve.” So, the theory of Evolution could not be considered as here being taught.

The Pope does not endorse the Big Bang when he says, "The Big Bang, which nowadays is posited as the origin of the world, does not contradict the divine act of creating, but rather requires it." He is simply saying that the Big Bang, a currently accepted scientific theory posited as the origin of the world, does not rule out a creating God, but requires it. So, the Big Bang theory could not be considered as being taught.

The Pope realizes he is not a scientist and does not debate with scientific theories. He addresses these theories the scientific community has provided from a philosophical and theological perspective and makes conclusions, e.g. they do not rule out the idea of a creating God.

Even statements such as "... And so creation continued for centuries and centuries, millennia and millennia, until it became which we know today...", and "The evolution of nature does not contrast with the notion of creation, as evolution presupposes the creation of beings that evolve.", are not meant to be taken as Church teaching. His remarks are not focused on these scientific descriptions as being something true, but he uses the description that the theories provide in order to show that they do not rule out the idea of creation.

A careful reading of his remarks will show that this is the reason for his remarks, to show that these scientific theories do not rule out the idea of creation, and this is the only new thing in his remarks that could be likened to a teaching. You can not teach something just by mentioning it, or accepting it for the sake of showing something else.

Popes write books, they answer reporters questions, they make speeches at various events. Not everything a Pope says is 'official'. When a Pope wants to provide anything that would be official teaching it is done in a way to make clear to all that this is the case.

The answer to your question is "No."

At least in what was quoted in OP, Pope Francis did not say the Big Bang is true, nor did he say the Theory of Evolution is true.

Essentially, he said that IF they are true, there still had to be a God to make them happen.

EDIT: Just to clarify - I did not explain what the Pope meant, only what he said.