Do you plan on remaining in Japan into your old age?
Are you going to stay in Japan forever?
If you 'settle' somewhere it is with a view to staying there. If you stay somewhere 'into your old age' the implication is that you will die there.
The third example is the bluntest.
「settle (somewhere)」は、そこにとどまる、落ち着く、ことを表します。「(stay somewhere) into your old age」で、死ぬまで（そこにいる）というニュアンスになります
3つ目の例が一番率直な言い方です。
You can ask:
-Do you plan on living in Japan indefinitely?
-Do you plan on moving back to your home-country?
-How long are you planning on staying in Japan?
以下のように尋ねることが出来ます。
-Do you plan on living in Japan indefinitely?
ずっと日本で暮らすつもりですか？
-Do you plan on moving back to your home-country?
母国に帰る予定はありますか？
-How long are you planning on staying in Japan?
日本にどれくらいの間滞在するつもりですか？
Three examples all asking for the same information.
First has simple question word what before the verb are(to be) linking it to the subject complement,your plans for the future.
Second and third are questions formed by using helping verb and main verb with the subject(you) in between. Do (you) see and Will (you) move. Both acceptable ways to form questions
3例とも同じことを尋ねています。
最初の例では、疑問詞「what」を「be動詞（are）」の前に、主語には「your plans for the future」を使っています。
二つ目と三つ目の例は［助動詞＋主語（you）＋動詞］という並びです。
どちらも質問文を作るときに使える型です。
Do you ever plan to return back to your home country?
The first question here uses the word "forever" which means for all future time. If the person answers "yes" then that means they are planning on staying in Japan 'forever' and never returning home. The second question is simply the opposite. Using the word 'ever' means 'any time in the future'. If the person answers 'yes' to this question, it means they will go back to their home country at some point.
If you're talking about travel, or how someone has visited a place, and you ask them if they plan on staying, they'll know you mean permanently - as in "Will you be staying in Japan permanently?" "Staying" implies permanently. But if you don't want to be so direct about it, you could ask something like, "Do you see yourself living here long-term?" which could lead to an interesting conversation about pros and cons or why your friend is traveling in the first place.
その人がどうしてその場所を訪れているのか話しているときに、"Are you planning on staying ..." と尋ねれば、永住するつもりなのかどうか尋ねていることが相手に伝わります。
例えば、"Will you be staying in Japan permanently?"（日本に永住するつもりですか）のように。
"Staying" には「永続的に」というニュアンスがあります。
ただ、もしそこまで直接的に聞きたくないなら、次のように言うこともできます。
"Do you see yourself living here long-term?"（自分が長くここに住むことになると思いますか）
このように尋ねると、メリットとデメリット、あるいはそもそもなぜ旅行をしているのかなど面白い会話に展開するかもしれません。
If you do something for the rest of your life then you say 'forever' so to ask your friend 'are you planning on taying in Japan forever? this means for the rest of their lives
To settle means to stay and live somewhere for a very long time
何かを残りの人生ずっとするなら、'Forever' が使えます。
'Are you planning on staying in Japan forever?'（日本に永住するつもりですか）
これは「残りの人生ずっと」という意味になります。
----
'To settle' は、ある所に長期間滞在・住むことをいいます。
Are you going to stay in Japan or move back home one day?
If you want to ask your friend if they plan to live in Japan or eventually go back to their country, you can say:
"Do you plan on staying in Japan?"
"Are you going to stay in Japan or move back home one day?"
このまま日本に住むのかそれともいずれ母国に帰るのか相手の予定を確認したいなら、次のように言えます。
"Do you plan on staying in Japan?"（日本にとどまるのですか）
"Are you going to stay in Japan or move back home one day?"（日本にとどまるのですか、それともいずれ故郷に帰るのですか）
イギリス 
日本 
南アフリカ 
アメリカ合衆国 
