Teaching presence as defined by Garrison, Anderson, and Archer (1999) is crucial when establishing a community of inquiry. It is therefore important that Trinh be able to respond promptly to any queries and have her presence felt by the students, without it becoming a burden. I would suggest a two-fold solution; first by carefully transferring over some responsibilities to the participants and the website itself and second to establish something similar to office hours.
I would highly recommend that Trinh first consider the questions and queries that she is receiving. She needs to determine if these should be addressed directly to her as a teacher or whether technical support or a well-designed FAQ could help divert some of the incoming mail. Equally she could establish, if not already done so, a place on the course website where people could ask questions to the entire group. This hopefully would alleviate some of the emails by sharing the facilitation responsibility (Garrison et al., 1999) with the other participants of the class.
The second part is establishing a fix session in which her students can reach her online through a live forum, collaborate or google hangouts. The transcripts of these online discussions can be saved and shared; hopefully alleviating some of the communications.
References:
Garrison, D. R., Anderson, T., & Archer, W. (1999). Critical inquiry in a text-based environment: Computer conferencing in higher education. The internet and higher education, 2(2), 87-105.