F is an English-speaking native, and J is F's colleague. F has just read the draft of a document which J wrote, and gives J a suggestion for improving it.
思われる omowareru
Giving someone advice or a suggestion requires an extra effort not to hurt pride or feelings. In this dialog, note that F has been very careful, using the V-(ra)reru form, which indicates that: (1) F is being honorific-polite to J (i.e. kaerare-ru instead of kae-ru to describe J's act) and (2) F's thinking/feeling is a natural occurrence (i.e. omoware-ru/kanjirare-ru instead of omou/kanji-ru).
あのうですね anoo desu ne
Anoo desu ne (F1) does not mean anything substantive, anoo being a hesitation noise and desu ne a filler. Like "you know" in spoken English, which is often inserted between phrases, desu ne (distal-style) and ne (direct-style) are used similarly in Japanese.
わけ wake
Regarding the Nominal wake, it means "reason" or "background". Therefore, mooshiwake literally translates as "a reason to say" or "an excuse", but mooshi (the stem of moosu) is a humble-polite Verbal, so mooshiwake arimasen constitutes an expression of apology, such as "there is no (humble) excuse" or "I'm sorry". In later Lessons, however, you will learn that wake has much wider and abstract usages related to the meaning of "reason".
スピーチ supiichi
As stated in this Lesson's KK, Japanese people tend to deliver speeches or write reports by first giving the general background or reasons which will later lead to the conclusion. This acutely contrasts with typical English speech delivery in which the conclusion or the speaker's position is given first, followed by the explanation supporting this position. Apparently from the listener's point of view, the latter method is easier to follow or monitor. This seems to be one reason why the Japanese language is often referred to as vague or obscure. This is not true. Every language is vague and obscure in one way or another, and there are ways to be precise if need be, in Japanese as well.
自然 shizen
Shizen means "nature" in English. When it refers to Mother Nature, it is a no-Nominal; hence, shizen no hon means "a book about Nature". But shizen may also be a na-Nominal referring to the state or manner of being natural; hence, shizen na iikata/hyoogen, meaning "a natural expression".
アドバイス adobaisu
Adobaisu is obviously a loanword from the English word "advice". As always, however, the original meaning has been somewhat distorted. Adobaisu in Japanese refers to a suggestion or advice given out of kindness or friendship.