Travelling From Taipei to Hualien to Taichung and back to Taipei

I will be travelling to Taipei during 24 Dec - 30Dec. My plan is to go Taipei to Hualien to Taichung and back to Taipei. May I know the weather, whether it's ok to travel to Hualien . I would also like to know how do I get to Taichung from Hualien, and where can I book all those train tickets. Can you suggest the best way to go? Thank you