The cess of majesty Dies not alone, but like a gulf doth draw What’s near it with it;

I think, Rosencrantz, it’s probably not good etiquette to mention the king’s death to the king, even philosophically. No one’s particularly keen to be reminded he is going to die, but especially kings and (you can’t know this) but especially kings who have committed regicide. So you’re reminding him, Rosencrantz, of not only his OWN death but the death of the previous king, his brother.
It’s just not good form.

But much more That spirit upon whose weal depends and rests The lives of many.

Weal is a funny word – because, when spoken as this is meant to be, it sounds just like “wheel” and in meaning, yes, weal, as in well being might actually make more sense – but as a metaphor, the many lives might just as easily roll along on the spirit of a wheel. like a train or a car.
And in fact, when this speech gets going, it goes EXACTLY there. There is a weal, then a wheel – like Rosencrantz got to the wheel metaphor from using the weal one. Now all we’d need to get a real confusing pun-tastic speech going is to get someone with a little speech impediment to talk about something real. You know, someone who can’t really say his Rs, so he talks about shows that are weally weally good.

The single and peculiar life is bound With all the strength and armor of the mind To keep itself from noyance;

My particular single and peculiar life
Does not seem quite free from noyance

Is anyone’s life free from it?

A noyance – free life would be so swaddled in cotton, there’d be no edges – and at a certain point, the cotton itself would become a noyance.

I had a book of Andy Warhol quotations and for some reason a line of his about rich people and problems stuck with me. It was something like, “Everyone has problems. Even rich people – even if it’s just that the toilet doesn’t work.”
Which frankly would be a bigger noyance for the poor as it will take either more time or a larger percentage of an income to fix it. But it is a noyance in any case.

But – any single, peculiar life does STRIVE to keep itself free from noyance. Even the simplest life forms move toward the nice things away from the not nice. We have movement and brains to help us do just that.

Most holy and religious fear it is To keep those many many bodies safe That live and feed upon your majesty.

So the king is the host
And his subjects are the parasites?
Is that how it goes?
The king is the cat
And the people are the fleas?
The king is the swimmer
And the people are the leeches?
The king is the ant
And the people are the zombie roaches?
It’s kind of weird analogy, Guildenstern.
Unless he means it in the sense
Of the body of Christ –
That is that all the people
Drink his blood and eat his body, like, spiritually.
Which is really just as weird
When you think about it.

We will ourselves provide.

There’s a double meaning in that.

There is the sense that they will step in and take care of the king’s needs. And there is also the sense that they will provide for themselves. And that they will deliver to themselves what THEY need. All things are true at once.
That is, they will be both self-serving and serve the king, simultaneously. I’m not sure which Guildenstern intends to say. (My money’s on serving the king – but he gives away his true motives simultaneously.)

The terms of our estate may not endure Hazard so near us as doth hourly, grow Out of his brows.

I picture a little flashing triangle pulsing its way out of Hamlet’s forehead – as if he had the Hazard symbol from a car emerging out of his head.
Danger! Danger! Danger!
It starts as a small quiet light, just a dull pulse – but as the hazard gets bigger – the triangle begins to become clear and eventually, he becomes one giant flashing warning.
Also – note Claudius’ language shift, in this little exchange. He starts with some plainspeaking and by the end here, he’s returned to doublespeak political phrasing. Such an interesting speech pattern our good king Claudius was!

I your commission will forthwith dispatch, And he to England shall along with you.

I would like to know more about this commission. What exactly are Rosencrantz and Guildenstern getting for their betrayal of Hamlet? It is a lot of money?
A commission, even now, might signal a parcel of money. But it may also be a long term gig – like a job- like he’s hired them to be representatives in England. So it may not just be a stack of cash but a steady paycheck for a long time.
Was this commission on the table from the beginning? Like, we’d like to hire you to be our representatives in England – which carries with it housing, a salary, a per diem and a lot of status. All we want you to do is come see how Hamlet is doing,

In other words, has this been the endgame for Rosencrantz and Guildenstern all along or is this just the next link in the chain?

I like him not; nor stands it safe with us to let his madness range.

The change from first person singular to first person plural in the middle of this sentence is very interesting to me. It feels like the first bit is a kind of honest blurt and then he calls himself to a less revealing stance. It’s like he switches from person to king in the middle of the sentence. Like, he suddenly remembers he’s the king.
It is also interesting that he pitches the real danger as to himself – which is true. He is the only one Hamlet really has it in for – but it’s funny that he reveals that to Rosencrantz and Guildenstern. I mean, if they think he’s legit crazy, he’d be a danger to everyone not just the king. However –

How in my words somever she be shent, to give them seals never, my soul, consent!

Happy Mother’s Day, Gertrude!
Your son got you a scolding for your special day. Isn’t that what every mother wants? A little shaming from her son?
At least, though, he’s not gone totally bonkers and even though he was afraid he’d be tempted, he has NOT also gotten you some matricide – so. . .something to Be Grateful for!
Some sons get their mothers flowers or chocolate – at the very least, a card. This son gets his mom some sharp words. What a prince!