Hmm okay, these things can be quite subjective, but here goes my opinion:
How does this text explore the issue of discrimination?
이 텍스트는 차별 문제를 어떻게 탐구합니까?
In my opinion, 탐구 doesn't sound that natural here, even though dictionaries list it as the meaning of "explore". (I think 탐구 is usually considered a dynamic activity, like how a scholar may explore multiple issues related to the central problem, but here we already have a finished text - it's not going to explore anything any more, it's the result of exploration.)
Also, 차별 문제 sounds a bit too terse, like "discrimination problem", while "the issue of discrimination" makes explicit that discrimination itself is the issue here.
I'd paraphrase it as: 이 글에서는 차별이라는 (문제/이슈)에 대해 어떤 관점을 제시하고 있습니까?
Compare this content with how issues such as national and cultural identity and discrimination can be seen to be explored in media (e.g. news reports, social media, movies…).
이 내용을 [[매체(뉴스, SNS, 영화 등)에서 보일 수 있는] [국가 및 문화적 정체성이나 차별 같은 주제에 대한] 탐구]와 비교해 보십시오.
Because of different word orders between English & Korean, your Korean translation contains an expression (매체...에서 보일 수 있는) which is awfully far away from what it modifies (탐구). Such long-distance relations generally make it hard to understand the sentence, in any language. We can rearrange it to flow better:
이 글의 내용을, 국가적/문화적 정체성과 차별 등의 문제를 (뉴스, SNS, 영화 등의) 매체에서 일반적으로 다루는 방식과 비교 설명하시오.
The original "can be seen to be" is rather verbose and honestly I'm not sure what the author intended, but "보일 수 있는" is not applicable here, because these issues (or rather, how they are handled) are seen by the reader (like you and me) - it's not about the media being able to show something. I think the whole thing is better explained by just adding "일반적으로" (generally).
Again, I don't like 탐구 as a translation of "explored", so I replaced it by 다루다 ("handle" or "deal with").
How this is affected by context?
맥락은 이러한 경험을 어떻게 영향 주게 되는 것 같습니까?
To be honest, I'm not sure what the author means by "context" - it seems, well, out of context here. Exactly what kind of context are we talking about? Maybe "context" itself is a sociological jargon here?
So I'm not sure what's the best translation here, but the rest of the sentence can be improved as:
맥락은 이러한 경험에 어떤 영향을 (끼칩니까/줍니까)?
"어떻게" instead of "어떤" is probably fine, but 어떤 sounds a bit better to me. The meaning is practically the same: "How does it affect ..." vs. "What effect does it have on ..."