I am a native korean. I hope I can help you guys and be helped with English. I’d like to join the group chat. What do I leave? Phone #?

....기 may contains basically a manner of time(tense) or planning.

For example, (나중에) 운동하기 (exercising (later)), or 10시에 운동하기 (exercising at 10 o'clock)

so that, ....기 involving tense or planning is a complete sentence ended by ...기

....는 것 contains the meaning of a conduct

For example, 운동 하는 것 (exercising or to exercise)

...는 것 can be easily defined as conducts.

However, ...기 is complicated. If you add a suffix (which can be added to a noun and makes it the subject in a sentence), then it becomes interchangeable with ...는 것.

For example, 운동하기가 어렵다 (it is hard to exercise)

As this example shows, ...기 + 가 makes it a conduct.

And also, ....는것 + a suffix is only implying a conduct.

In short, ...는 것 is very clear to use, and if ....기 is used as a subject then both are interchangeable

if a phrase ends with ....기 then it contains time, so what I suggest you is to use no matter what you choose.

Oh, additionally, after all this comment, I realized that ....기 also includes one's expectation.

If your girlfriend ask you 10시에 운동하기 then she expect you exercising at 10 o'clock, and my reply from your first question indicates 가져오 기를(길) 원했다 also includes your girlfriend's expectation.

Anyways, you can use either. the use of ...기 including time, planning, or expectation is likely 10%-20% of all time I guess.

Your translation is exactly correct in terms of literal ways. I don’t want to confuse you because of various way of expressions, but if you want an express more natural and nonliteral way then ‘내 여자친구는 (내가) 사과를 가져오 길 원했다.’

Here is the explanation.

If you use 내, 네, or someone’s name without a suffix that indicates the subject and following by another noun can mean my, your, or someone’s. For instance, 내 가방, 네 가방 , or Raphael 가방 mean my bag, your bag, Raphael’s bag

(내가) is not necessary unless your girlfriend specifically wanted you to bring the apple among people. If your girlfriend wanted an apple and if the person who was willingly to or had to bring an apple is inevitably you, or when you talk to someone, if the person think that the person who brought an apple is absolutely you, then it is unnecessary to say it, but you can still say it

~길 you can say that instead. It is kinda similar way to express ‘get’em all’ which means ‘~길 = 것을’

(Sentences implying wanting, hoping, or wishing ONLY)

Hope you understand this. If you don’t, any question is welcomed.

Furthermore, I have read your question somewhere else in italki. You are studying 는 것. It is the same as verb + ing or to + verb which transform verb to noun for 100% sure (honestly, I can think of for now, and also you may not agree with the thing defined as transforming)