Today, I focused on reading past articles written in English to be prepared for the exam upcoming upexam. Today, I focused on reading articles written in English to prepare for the upcoming exam.

"reading past articles" doesn't make sense. Do you mean "reading articles I wrote in English in the past" or do you mean "reading various articles written in English"?

Today, I focused on reading pastthe articles [I have read/ I read] [in the past], which are written in English, to be prepared for the exam upcoming upexam. Today, I focused on reading the articles [I have read/ I read] [in the past], which are written in English, to be prepared for the upcoming exam.

ところで、過去形を使ったので、[in the past]はいらないかもしれません。 代替案：Today I focused on reading articles written in English to prepare for the upcoming exam.

Honestly, I would like to read an article about Brexit,(,) but I don't have time. Honestly, I would like to read an article about Brexit(,) but I don't have time.

Comaがない方が自然に聞こえますが、Rubyさんが書いた文章は問題ないです。