At last, I’ve finished my first week’s work! This week I did a lot to prepare for the new term, and classes start next week. Although I got off work on time, I had so much to do after work that it caused me to sacrifice precious sleep time. I need to raise my proficiency in order to make room for sleep time. Otherwise, keeping my eyes open the next day becomes difficult. I’ve gone to the dance studio four times, finished reading a book, and maintained my learning habits this week, so I feel myself worthy of praise. I changed "finally" to "at last" to avoid duplication with "finished" Changed "I've done" to "I did" because you are reporting what you did. If you say "now" instead of "this week", it makes sense to say "I have done". The present perfect pattern talks about the present, not the past. That's why it makes sense to say "now I have done". You could also say "looking back on this past week, I have done ..." and that makes sense because you are looking at this present moment. "will start" is fine, but "start" is simpler. Your third sentence needs a time frame. When did you get off work? When did you have so much to do? The meaning is not clear. "maintained" is better than "kept" because "maintain" feels more active. It comes from a Latin root meaning "hand" so "maintain" has the feeling of "hands on". You could also say "I deem myself praiseworthy".

Finally, I’ve finished the first week’s work! This week I’ve done a lot to prepare for the new term, and classes will start next week. Although I finished work on time, I had so much to do after work that I had less time to sleep. I need to improve my efficiency so that I time to sleep; otherwise, I’ll have difficulty keeping my eyes open the next day. I went to the dance studio four times, finished reading a book, and kept up my learning habits this week, so I feel I’m worthy of praise.