I know of no reliable evidence that differences between human languages correlate significantly with, let alone cause, differences in human cognition. That said, I do expect it's easier to coordinate activities within a group that has language devoted to the nuances of such activities, and that's as true of rationality as anything else. But I also expect that sort of jargon is no harder to construct in one natural language as another.

It seems that in weak formulations it can be confirmed.

Have you read "Through the Language Glass" by Deutscher?

Choosing better words for some situations does train you in some skills. It looks like people distinguish colours quicker if they have different names. For example, Russian speaker will notice the difference between "closer to sky blue" and "closer to navy blue" faster than English speaker because of habit to classify them as different colours. Deutscher cites a few different studies of that kind.

Apparently, language can also change your default reactions (how you interpret omissions) in the sense that you can set up some scene on the table, then lead a person to another room and ask which table has the same scene as in the first room; whether the language uses north/south or left/right for path descriptions can be seen by answers.

As for applications, it seems to say what you would try anyway — if you want to improve awareness of somethingm encourage saying it out loud every time.