As of currently, there are no flights between CNX and Hong Kong. On booking sites, Hong Kong Express has flights scheduled from November but they haven't made an official announcement yet and that would also depend on any restrictions in Hong Kong. If op wants to transfer in North Asia, Korea would be better and there are regularly scheduled flights to CNX.
United doesn't fly to Thailand - why would you think there is a United Terminal? this isn't the US. You can catch domestic flights from BKK to CNX though with no hassles.
buring season proper starts towards the end of February as the weather changes and traditionally ends around Songkran in April - can be early or late April, though depending on the year.
You can see the bad months in the pollution data. March everyone agrees is best avoided although this year was just weird due to the early rain.
Relative to what you consider modest to be. There was a guy a few years back who was boasting and making videos about how he lived in Chiang Mai on only US$300 a month but he lived in a Thai dog box condo and cooked his own rice to take to restaurants to keep the bill down. You can live on that amount but unless you are absolutely desperate, why would anyone want to?
However, if you had say US$1,000 a month which for some is modest, you can live a fairly comfortable life.