]all the uses of this world!

]'tis an unweeded garden,
That grows to seed; things rank and gross in nature
Possess it merely.

] Is Denmark the unweeded garden, or is it "this world" in general? We already know that more people than Hamlet think that "something is rotten in the state of Denmark". Is he just re-interating that theme?

]Is regicide a sin so great it's like original sin, filling Eden with "things rank and gross"?

I think it is a reference to the particular circumstances, but also to the whole idea of human nature, original sin and the whole garden of Eden/paradise lost kind of motif that recurs.

There are other references made to the garden of Eden, human nature and the original sin:

When the ghost tells Hamlet how he was killed, he says "a serpent stung me"

In 3.1 Hamlet tells Ophelia:

"...for virtue cannot so inoculate our old stock but we shall relish of it."

The notes in my Hamlet edition say that 'inoculate' is used in a horticultural sense there, as in grafting a plant with different qualities than the original on to the old stock, and the implication there that human nature and its tendency toward original sin cannot be escaped.

Claudius, in his "O my offense is rank" (echoing Hamlet's use of the word rank!) speech in 3.3 also makes reference to the Adam and Eve story: "It hath the primal curse upon't--A brother's murder" and this fits in with Hamlet seeing Denmark as not the kind of garden it once was, as in the bible once they were no longer in Eden, the first sin was one brother murdering another.

Hamlet again makes a reference to the whole Adam and Eve/garden of Eden story in 4.4 in his "How all occasions do inform against me" speech.

"...Sure he that made us with such large discourse,
Looking before and after, gave us not
That capability and godlike reason
To fust in us unus'd."

In the creation stories, the ability to think and reason was what separated humankind from the beasts, and yet ultimately what drove them from the garden or from paradise, because they were tempted to become 'godlike' in desiring to eat from the Tree of Knowledge or to know that which they were not meant to know.