かどうか: put a question inside a sentence
Distinguish whether something is true from questions asking who, where, or when. Turn that question into the content of checking or knowing.
Keep both yes and no possibilities open
明日、店が開いているかどうか調べます。 means checking whether the shop will be open tomorrow. かどうか packages the proposition 開いている.
With present affirmative nouns and na-adjectives, normally omit だ: 学生かどうか and 便利かどうか. Do not learn 学生だかどうか as the basic pattern.
Use か when a question word is already present
店が何時に開くか調べます。 means checking what time the shop opens. Because 何時 asks for a time, this embedded question normally ends with か.
誰が来るか分かりません。 likewise means not knowing who is coming. First decide whether you need a yes/no answer or information such as a person or time.
Specify what remains uncertain
この道でいいかどうか分かりません。 says you do not know whether this route is right. It identifies the uncertainty more precisely than 道が分かりません.
Do not insert the direct question この道でいいですか。 unchanged into another sentence. Package it as この道でいいかどうか before adding 調べます or 確認します.
Quick check: In 電車が何時に出発する（ ）確認します, do you need か or かどうか to check what time the train departs?
Show the answer and why
Use か: 電車が何時に出発するか確認します. 何時 already asks for a specific piece of information.