First of all one correction: After a verb you don't need の so it's あきらめないように Also 2 ように in 1 sentence is possible, but no one talks like that because it's confusing. Also also, you have to be careful about the nuance. 食べるように料理する sound strange (because people will want to eat if you cook or not). Your cooking will not change a person's mind about eating. あきらめないように何かする is ok because you can change a person's mind about quitting or not. So, use ように when you can control the situation. When you want to control somebody or make them do something you want. Anyway this sounds better: 絶対あきらめないようにいっぱい注意させてください。

Cost. Because 1) you already paid for it before you could sell it 2) costs doesn't sound natural in this context If you use "costs", you're saying that you sold it for more than its worth at time of sale, meaning you ripped off the buyer

Answer to question 1 Japanese people don't like to be frank and they don't say things straight (especially when it's something they CAN'T do). So instead of saying "I really just can't do it" they say "For me, there aren't any options to do anything". This sounds like they still want to help you but they just can't. If you say できないよ it may sound like you don't care. Answer to question 2 After trying to use のない in Japan for 10 years my advice is don't use it. Nobody speaks like that and I almost never see it in writing.

what song?

Korean people are nice but busy. Maybe they really don't have time so don't worry. Keep on looking and you will find someone who is interested to do language exchange with you. I usually have to speak to 10-20 people to find just 1 person. It's normal.

Here is what I did in order: 1) listen to Japanese songs 2) learn all hiragana/katakana 3) get a textbook and learn basic grammar 4) get a dictionary and start learning kanji 5) get Japanese friends 6) get Japanese roommates 7) get a Japanese bf/gf 8) do Japanese arts/sports 9) read books in Japanese 10) move to Japan 11) work at a Japanese company I was never obsessed with Japan. I really did all that stuff to become good at Japanese asap and it was a lot of fun as well.

It's translated as "to accept an unfavorable situation" so I would say "to come to terms with" for general situations