Can a foreign university file a PCT Chapter II demand directly with SIPO acting as IPEA?

I am Japanese Patent Attorney, only qualified for filing international patent application to Japan Patent Office acting as Receiving Entity, or as patent office of designated country. So please understand that I cannot guarantee my answer is correct when your case involves filing to Thai patent office and demand preliminary examination to SIPO.

Filing to SIPO?
PCT A. 31(6)(a) ---> you should file the demand to international examination entity.
It should be the foreign Patent Office that Thai patent office designates as international examination entity.
Please ask Thai patent office if SIPO is the one.

See Box No.III "agent"
http://www.wipo.int/export/sites/www/pct/en/forms/demand/ed_demand.pdf

It looks like anyone in any country could be agent for filing a demand.

(But I am not quite certain. Usually, we see attorney, in the country of the examination entity (SIPO), acts as agent. In your case Chinese attorney, not Thai attorney.)

If so, what payment routes are available?
Payment should be made to Examination entity, in your case SIPO, if Thai patent office, acts as receiving office, designates SIPO as Examination entity. (PCT Rule 57.1)

How can status be checked?
https://patentscope2.wipo.int/search/en/search.jsf;jsessionid=66D0E821F2282970E6A0E27C409BDFFF

You type in WO publication number, application number, etc, in the box and press search, you can get various information.

According to China Patent Law and Patent Examination Guidelines, if foreigners/foreign enterprises, without habitual residence or business premises in China apply for patents or handle other patent-related matters (including international application entering the Chinese national phase), they shall entrust lawfully established patent agencies in China with such matters.