Will you be taking that day off or will you go there after work?
未来の予定の話なので未来形を使われます。英文の最初の部分は "will you be taking that day off" を書いています。これは日本語に翻訳すれば、「その日は仕事休みしますか」を表します。そして、"or will you go there after work" は「それとも終わってから行きますか」という意味。
日本語書いた質問は2つがありますけれども、英語で "or" を書いたら、繋がれる。ですので、1つ文章になりました。
Do you have the day off or are you going after work?
A "day off" is a day in which you don't work. Normally these refer to holidays or vacation days. This is used in American English. I hope that this helps. :)
Do you have the day off? or are you going after work?
Will you be taking the day off or going after work?
To not go to work as you have planned to have it off to do something is called a 'day off' as you are not going there
Taking the day off means you are taking a day off from work and doing something else
仕事の休みを取ることは、'day off' といいます。'off' には「離れて」の意味があります。
'taking the day off' は、仕事の休みを取って、何か他のことをすることを言います。
"Do you have the day off? Or are you going after work?"
"Will you be taking that day off or will you go there after work?"
"What is your plan, to take the day off or go up after work?"
If your friend has said that they are going shopping on Black Friday and you wanted to ask when, you could say any of the following: "Do you have the day off? Or are you going after work?", "Will you be taking that day off or will you go there after work?" or "What is your plan, to take the day off or go up after work?".
友達がブラックフライデーの買い物に行くと言っていて、いつ行くのかを聞きたいときのフレーズです。
"Do you have the day off?
（仕事休みなの？）
" Are you going after work?"
（仕事の後に行くの？）
"Will you be taking that day off or will you go there after work?"
（休みを取るの？それとも仕事の後に行くの？）
"What is your plan, to take the day off or go up after work?"
（仕事を休むか、仕事の後に行くか予定はどんな感じ？）
If you know your friends usual working hours, you could simply ask your friend "What time will you go?" and see if you can determine whether they may intent to have time off work or if they will be going outside of work hours to shop on Black Friday.
If you do not, you could ask them by offering the two alternatives:
EG:
"Will you go shopping for Black Friday during work hours or will you go after work?"
相手の普段の勤務時間を知っているなら、シンプルに "What time will you go?"（何時に行くの）と聞けます。その答えによって、休みを取るのか勤務時間外に行くのか分かりますよね。
もし知らないなら、二つの選択肢を提示できます。
例：
"Will you go shopping for Black Friday during work hours or will you go after work?"
（ブラックフライデーの買い物は勤務時間中に行くのですか、それとも仕事が終わった後ですか）
アメリカ合衆国 
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