When doing an outland application, you can have it processed either at the visa office responsible for your country of nationality or at the visa office responsible for the country that you have been lawfully admitted to for at least one year. That is NOT the same as living there for one year. In your case, this means your husband can have the application processed in Thailand if the visa he's there under does not expire for another year. How long he has lived in Thailand doesn't matter, they will only process it there if he will be allowed to live there for at least one more year, meaning his visa doesn't expire for another year from the time you apply.
The medical can be taken anywhere in the world. If you're doing it outside the processing visa office's region though, it's a good idea to include a note saying where you did take it. That way the odds that they will look for the results in the right place are better.
The visa office will ask your husband for his passport - the visa they issue when the application is approved goes in the passport, so it's essential that he sends it in.
I'd suggest you look into everything else he needs to see if he can get that from Thailand (police certificate etc). You can read the guide for applying through the Phillipines here: http://www.cic.gc.ca/english/pdf/kits/guides/3905e.pdf
He will also need a police certificate from any country where he's lived in for 6 months or more since turning 18.
You can find the current processing times here:
http://www.cic.gc.ca/english/information/times/international/05-fc-spouses.asp
Looks like 4 to 8 months for Manila, 5 to 14 months for Singapore. My guess would be you're better off with Manila.