'one third' is simply a single unit of 'third'. Two or more and we use 'thirds'; hence, 'two-thirds' is the correct usage.

Is two thirds grammatically correct?

Two-thirds is normally a noun, as it is in every sentence in post 3. In every case "two-thirds" is part of a noun phrase and it is the noun phrase which is the subject. The choice of plural or singular verb was explained in post 2.

How is two thirds written?

For example, you can write two-thirds in fractional form – 2/3 – or as a decimal – 0.667 – and either way, you calculate two-thirds of a number by multiplying by that number.