I don’t know the Chinese language at all, but through a google image search was able to find articles written in the language. I believe this is how Chih-Kai Lai’s name is written, if you want to search yourself for news articles:
"賴致愷"
From various articles this is what I can piece together, which may not be accurate due to google translate’s imperfect translations:
Chih-Kai came to the US on July 24, accompanied by his father (and aunt, I think). His father remained here in the US with his only son until Aug 1, when the father returned to Taiwan after getting his son settled in his dorm, and all seemed fine.
Chih-Kai had a roommate until Aug 14, but because it is “a temporary dormitory” he was alone from the 15th to the 18th.
All his baggage was still in his room, with only his cell phone missing. His bank account does not show any abnormal withdrawals.
On Aug 17, he had contact with his family.
On Aug 18, he used cash and ate somewhere.
Aug 19 was the first day of classes at Auburn, and Chih-Kai did not appear, which was when he was noted as missing.
Here’s a link to one Chinese language article on Chih-Kai:
影/失聯前都正常 北科大:賴致愷是獨子,阿嬤不知道孫失蹤 | ETtoday新聞雲