Yes. Here are two examples from famous poems that use similar wording. From "The Rubaiyat of Omar Khayyam," as translated by Edward FitzGerald: "Ah, make the most of what we yet may spend, <---as in "to spend time" Before we too into the Dust descend." <---i.e. to die "To the Virgins, to Make Much of Time" (by Robert Herrick), the title of a poem. It means the same thing as "Make the most of your time." The poem begins: Gather ye rosebuds while ye may, Old Time is still a-flying; And this same flower that smiles today Tomorrow will be dying.

Absolutely. "Make the most of your life" is a very common phrase, as is "make the most of your day", "make the most of your vacation", "make the most of the opportunity", etc!

Do you mean "contexts"? And yes, you can. As long as the phrase involves some sort of time period, like a day, a month, a year, a lifetime and so on.