Notice that Gertrude asks what she should do; Hamlet, famous for inaction, tells her what she should not do.

By framing his response in the negative, Hamlet also forces them both to picture the forbidden action–the lovemaking that disgusts and apparently obsesses him–in further nasty detail.

bloat: bloated, fat.

Claudius has ordered Hamlet shipped to England on official business, even though all concerned know he is getting the unruly prince out of the way.

In fact, his true intention is to have Hamlet killed, as these “letters” will ultimately reveal. See 5.2.

i.e., Let Claudius’s plan go forward. Hamlet speaks here with almost gleeful bravado.

One last dark joke. Hamlet will be “drawing” (dragging) Polonius’s body away as well as drawing his interactions with the man to an end. Because the man is dead.

Hamlet dragging Polonius. Artist unknown

A complex joke. A “counsellor” (official advisor) is supposed to “keep counsel” (be discreet), but Polonius, according to Hamlet, was a foolish chatterbox. Now death has shut him up, and ironically made him better at his job.

“Grave” is of course a pun–Polonius is now solemnly quiet, and also dead.

Throughout the play, Shakespeare subtly brings Polonius’s and Hamlet’s talkativeness into parallel. The crucial difference is that Hamlet has much more of substance to say. Polonius’s “stillness” in death anticipates Hamlet’s final line: “The rest is silence.”

packing: (1) taking on a load; (2) leaving in a hurry" (Riverside Shakespeare).

A characteristic dark pun. Killing Polonius has two immediate consequences: he must dispose of the body and must be shipped off to England.

Continuing his heavy sarcasm, Hamlet says in effect: “No, no, go ahead and spill the beans to Claudius–and get yourself killed in the process.”

Where we would say “spill the beans” or “let the cat out of the bag,” Hamlet uses the image of letting birds fly from a rooftop cage. He then adds a reference to a “famous” (but now lost) fable about an ape who tries to fly–in this case, “experiments (to see whether he too can fly if he enters the cage and leaps out)” [Riverside Shakespeare].

https://www.youtube.com/watch?v=74Km12WacOk

Riverside Shakespeare glosses (2nd ed., p. 1217):

paddock: toad.

gib: tom-cat.

dear concernings: matters of intense concern.

Dripping with sarcasm, Hamlet is asking: “Why would a wise, sensible queen hide such important matters from such a disgusting man?”