What do we learn about the differences between the reality of Willy's life and the facade that he presents in Death of a Salesman?

This is an interesting question because it depends on the
context in which you are asking it.  Willie's "facade" isn't really a facade at all. 
Dictionary.com defines facade as "a front or outer appearance, esp a deceptive one"
There is a sense of intentionality here and I think that is absent in
Willie.

Instead, I think the problem is self-knowledge. 
When I think of Willie, I recall the words of "To a Louse" by Robert
Burns:

O wad
some Pow'r the giftie gie us
To see oursels as others see us
It wad
frae monie a blunder free
us

Of all
knowledge, self-knowledge is perhaps the most difficult to achieve.  Doestovesky, in
Notes From the Underground" makes a interesting a relevant
observation:

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"Every man has some reminiscences which he would
not tell to everyone, but only to his friends. He has others which he would not reveal
even to his friends, but only to himself, and that in secret. But finally there are
still others which a man is even afraid to tell himself, and every decent man has a
considerable number of such things stored
away."

The tragedy
in "Death of a Salesman" isn't that he puts up a facade, but that "he had all the wrong
dreams."  He though that, in the world of business, relationship meant something,
promises meant something ... that he meant something.  He learned, sadly, that man is a
piece of fruit --- you can, and we do, "eat the fruit and throw away the
peel."

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