Ｒｅｃｅｎｔｌｙ　Ｉ　ｓｔｕｄｙ　ｖｅｒｙ　ｖｅｒｙ　ｌａｔｅ　，ｊｕｓｔ　ｌｉｋｅ　ｔｏｄａｙ．　Ｉ　ｓｔｕｄｙ　ｄａｙ　ａｎｄ　ｎｉｇｈｔ！Ｂｅｃａｕｓｅ　ｔｈｅ　ｐｒｏｇｒｅｓｓ　ｏｆ　ｍｙ　ｐａｐｅｒ　ａｌｒｅａｄｙ　ｆａｌｌｓ　ｂｅｈｉｎｄ　ａ　ｌｏｔ，　Ｉ　ｗａｎｔ　ｔｏ　ｃａｔｃｈ　ｕｐ．Ｈｏｐｅｆｕｌｌｙ　ｍｙ　ｂｏｄｙ　ｉｓ　ｈｅａｌｔｈｙ　ｅｎｏｕｇｈ，ｈｅｎｃｅthen　Ｉ　ｃａｎ　ｈａｖｅ　ｍｙ　ｐａｐｅｒ　ｄｏｎｅ　ｉｎby　Ｏｃｔｏｂｅｒ　ａｃｃｏｒｄｉｎｇ　ｔｏ　ｍｙ　ｐｌａｎ．

"Hence" is very formal and old-fashioned, and "A hence B" usually means that "Because A is true, B is true." In your sentence, A = "Hopefully my body is healthy enough". This isn't a true and factual statement. It's a hope. So using "hence" doesn't really work.

Also, when talking about a deadline, we usually say we want something done "by" the deadline.

Ｉｎ　ａｄｄｉｔｉｏｎ，　ｍｙ　ｆｒｉｅｎｄ　ｍａｒｒｉｅｄ　ｔｏ　Ｔａｉｗａｎ　ｉｓ　ｑｕｉｔｅ　ｆｒｕｓｔｒａｔｅｄ．Ｓｈｅ　ｃｏｓｔｅｄ　ａ　ｌｏｔ　ａｓ　ｓｈｅ　ｂｏｕｇｈｔ spent a lot of money on　ａ　ｂｒａｎｄ　ｎｅｗ　MａｃＢｏｏｋ　ｆｏｒ　ｈｅｒ　ｎｅｗ　ｐａｒｔ－ｔｉｍｅ　ｊｏｂ．Ｕｎｌｕｃｋｉｌｙ，ｓｈｅ　ｌｏｓｔ　ｈｅｒ　ｊｏｂ　ｏｎｃｅ　ｓｈｅ　ｂｏｕｇｈｔ　ｔｈｅ　ｌａｐｔｏｐ！Ｉ　ｃｏｍｆｏｒｔｅｄ　ｈｅｒ　ｔｈａｔ　ｓｈｅ　ｗｉｌｌ　ｇｅｔ　ａ　ｎｅｗ　ｊｏｂ　ｓｏｏｎ　ａｓ　ｌｏｎｇ　ａｓ　ｓｈｅ　ｈａｓ　ａ　ｌａｐｔｏｐ．Ａｎｙｗａｙ，her ｌａｐｔｏｐ　ｍｅａｎｓ　ａ　ｌｏｔ！

"my friend married to Taiwan" -- I don't understand what this means.