Find x Find out x Discover

Today I created a post in which I wrote the following passage to explain my points related to my questions.

"Just give you a context about where I knew this expression, I discover it after finishing an unit of an English activity without making mistakes."

Here are my questions:

1°) Could I replace the word "context" with the word "background"? Do both words play similar roles?
2°) As far as I know, I could replace the word "discover" with the phrasal verb "find out", although "discover" add up more formality to the passage. By replacing the words I would have to write "find it out" instead of "discover it'. Is the expression "find it out" reasonable? It sounds weird to me.

COMO COMBINAR PALAVRAS EM INGLÊS
Nesta aula, o professor Denilso de Lima, autor do livro "Combinando Palavras em Inglês", ensina como as collocations (combinações de palavras) podem ajudar você a falar inglês com mais naturalidade. ACESSAR AULA
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Find out é descobrir no sentido de obter informação a respeito de alguma coisa em inglês.

No seu exemplo, as opções mais adequadas são:
Just to give you some context about where I found this expression. I found it after finishing a unit of an English activity without making mistakes.
Ou
Just to give you some context about where I came across this expression. I found it after finishing a unit of an English activity without making mistakes.
Onde find out deve ser usado:

She'd been seeing him for a while, but didn't want her parents to find out.
I haven't found anything out about him yet.
Can you find out what time the meeting starts?
I don't know when the game starts, but I'll find out.

Discover é realmente mais formal do que as outras opções.

Bons estudos.
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Muito obrigada, Donay. Entendi perfeitamente.