Would you write
He has been selected for testing the car
OR
He has been selected to test the car
OR
He has been selected to testing the best car ever made
Would you write
He has been selected for testing the car
OR
He has been selected to test the car
OR
He has been selected to testing the best car ever made
He has been selected for testing the car.
The above is grammatically correct. You are using the present participle as a noun as testing becomes a gerund.
He has been selected to test the car.
Also right, this is what most people would say.
He has been selected to testing the best car ever made.
The phrase "to testing" is both grammatically and semantically wrong.