There are some mistakes with your introduction. 我喜欢做朋友跟中国人 . 我喜欢和中国人做朋友。 因为我打 参加HSK考试，因为我打算参加HSK考试，

In my view,孤零零 is only one 寂寞 is lonely 独自是alone

Both 孤零零 and 寂寞 mean ''a feeling of loneliness'',and 孤零零 is a pattern,like ABB,it's more oral 独自 means "on one's own'' or ''do something alone''