1. "바쁘느라고" is kind of weird. "~느라고" must be put behind verb like 가다(go), 일(work) ex) 오늘 병원에 가느라고 점심 밥을 못먹었다. Since I saw a doctor, I couldn't eat lunch. Because "바쁘다" is adjective, it can't be combined with "~느라고" If you use "바쁘다(busy)", "~서/~해서" is better. ex) 오늘 너무 바빠서 휴대폰을 사용할 시간이 별로 없었다. 2. Both "~할 별로 없다" and "~하려고 별로 없다" is not right. A Noun must be put in front of "없다". In your sentence, "시간" is a noun, meaning time. "시간이 별로 없다" is correct I think you want to make "I was very busy, and I didn't have enough time to use smartphone" So, if you would like to modify "시간", you would put "사용할" in front of "시간" Therefore, you can make full sentence "오늘 너무 바빠서 휴대폰을 사용할 시간이 별로 없었어요."

No problem :) If you any questions, feel free to contact me later :)