How can one distinguish between permissible and impermissible means after having put one's trust in Allah? And are impermissible means referred to as polytheistic means, or not?

Causes are divided into permissible and impermissible. The permissible causes are every beneficial cause that the Shari'ah has not forbidden with a prohibitive prohibition. As for the impermissible causes, they are those that the Shari'ah has forbidden or whose causality has not been established. The Shari'ah defines causes as either legal, such as supplication, or sensory, such as medicines, and their effect must be direct, not illusory. Shirk in causes occurs by believing something to be a cause when it is not, or by relying on the cause while being heedless of Allah. This is divided into major shirk, which negates Tawhid, and minor shirk, such as relying on a cause while forgetting the Causer. There is also a category that does not negate Tawhid, which is relying on the cause while depending on Allah.