No. The form you are looking for is this: "This is useful not only in order to .... , but also in order to ...."

Yes. In example " This is useful in order, not only to run, but also to swim?" You speak English very well.

It’s “in order to”. Without “to” you just have “in order” which means everything is prepared or ready or arranged- a totally different meaning.

Greg's version is grammatically correct. Yours isn't. But I would recommend using another construction. It's wordy and awkward.