posted by Henry1 .
Could you please check these sentences, too? I tried to rephrase the first lines again.
1) Hamlet wonders whether it is better (for him) to endure the assaults of shameless fortune ("the slings and arrows of an outrageous fortune") or to fight against his mass of troubles.
2) He is doubtful whether to surrender (give in) to fate or to fight against it. /He is doubtful whether he sould surrender to fate. ...
2) Human beings are born (or bound?) to suffer.
3)He asks Hamlet to avenge him (also: to take revenge/vengeance on Claudius for his own murder /are they possible???) but to leave his mother’s punishment to heaven.
1. I'd leave out "shameless" but the rest is fine.
2. OK (watch the spelling of "should" however)
3. Yes, the variations are possible, but wordy. Your first phrasing is the best.