Learn English – What’s the difference between “horrible” and “horrific”

It depends on the context.

Use most to refer to a quantity of an unspecific group. We use most when we are speaking in general and do not have a specific group of people or things in mind.

Most students pass the test. (Speaking generally about an undefined population)

Use most of the X to refer to a quantity of a specific group. Note the expression includes a phrase defining the number to a specific group.

Most of the students (of my class/school etc.) passed the test. (Speaking about a specific sample of the population)

Ref: http://www.grammar-quizzes.com

Almost can be used with expressions of time and quantity. In other words you have to define the quantity.

Almost half of the students passed the test.

An interesting question. The two words are synonymous for the most part. However, wary has a bit more of an emotional component in it, a feeling of reluctance to do whatever one might be wary about doing. Cautious is more of a carefulness based on reason.

From the Merriam-Webster definition of cautious (the synonym discussion halfway down the page):

Cautious implies the exercise of forethought usually prompted by fear of danger. ⟨a cautious driver⟩ ... wary emphasizes suspiciousness and alertness in watching for danger and cunning in escaping it.