How we cite our quotes:
O, my offence is rank it smells to heaven;
It hath the primal eldest curse upon't,
A brother's murder.
Talk about major religious allusion: this is a reference to the biblical story of Cain and Abel. Comparing his sin of killing Old Hamlet to Cain's sin of killing Abel really ups the "major sin" factor of Claudius's treachery.
That skull had a tongue in it, and could sing once:
how the knave jowls it to the ground, as if it were
Cain's jaw-bone, that did the first murder!
Here, Hamlet is complaining that the gravedigger is being a little rough with the bones—only murderers deserve to be handled so roughly. This says a lot about our sensitive protagonist. Despite all his emo musings about death and suicide, Hamlet values life.
No more be done:
We should profane the service of the dead
To sing a requiem and such rest to her
As to peace-parted souls.
Lay her i' the earth:
And from her fair and unpolluted flesh
May violets spring! I tell thee, churlish priest,
A ministering angel shall my sister be,
When thou liest howling.
Since Ophelia's death is suspect, the Priest refuses to do anything more than the bare minimum for Ophelia. But Laertes isn't having it: he thinks that the stingy burial rites aren't doing Ophelia's memory justice. He understands what the priest doesn't: burial services are rituals for the living.