I have finally decided to amend the itinerary to be as follow:
Day 1 arrive Taoyuan at around 12.00 travel to Sun Moon Lake via bus/HSR/Nantou bus direct to SML
Day 2 Tour SML and Formosan Aboriginal Cultural Village to get there via ferry and transfer cable car or by bus
Day 3 Travel to Cingjing from SML in morning. Will it be better for me to travel via cab direct to Cingjing or take Nantou bus to Puli and transfer from Puli to Cingjing?
Day 4 Mt Hehuan in morning, Cingjing farm in afternoon, Lushan hotspring at night. Should I get E-go bus tickets which comes with entrance tickets or book a cab for the day?
Day 5 Travel back to Taipei. I have a question here, the bus direct to Taipei ( http://taiwanbus.emmm.tw/?ptype=info ) will only arrive in Taipei at 19.00. Is there a faster way for me to reach Taipei by 16.00? Or would it be better if I cab from Cingjing to Taichung HSR then take HSR to Taipei? What are the time estimates?
Lastly I am not very sure how to go about buying the bus tickets.
Should I get the Nantou bus tickets (from Taichung to SML) directly at Taichung HSR station?