No, most of the taxi drivers (in Bangkok) are not ethnic Thai, they are Lao-Isaarn.
Their language is Lao-Isaarn, not central Thai.

You do find a few ethnic Thais driving taxis in Bangkok, but not many.
In my experience, based on simple conversations, less than 5% are speaking central Thai.
I often ask the drivers what province they are from.
In two-plus years of riding in hundreds of taxis, only one has said he is from Bangkok.
Perhaps three or four have named provinces in central Thailand, and another few in the Northern provinces.
All the rest are from provinces in the Lao-Isaarn region.

I don't know about Chinese language, but some taxi drivers here have a smattering of Japanese.
I know because a few have practiced their Japanese language on me.
Why, I have no idea.

The problem with their English, is the Thai pronunciation of English words is very far from anything we would expect.
They add in their own tones and their own styles of vowel lengths and emphasis.
They think they are speaking English, but you are going to have a very difficult time understanding more than a word here and there.

-- Peter