Since HKBH wants him dead anyway, is he allowed to fulfill God’s will by taking his own life?
No, he is still bound by 7 mitzvahs of bnei Noach. I think it’s wrong to say Hashem wants him dead because then Hashem would arrange for it right away. Rather, Hashem wants us to fulfill the mitzvah for whatever reason.
Does the sheva mitzvos against murder apply to suicide?
Yes, suicide and even making himself bleed is included in it.
was it a good thing that Haman was killed even though it was a non-Jew who did it?
Yes it was a good thing but no one got the mitzvah for it.
Amalek is engaged in a bloody war with Moab. Do we go to war with the Moabites to stop them from killing the Amalekites so we can do it ourselves, or do we let the Moabites try anyway and say that’s it’s not worth Jewish blood to save the Amalekites if others are willing to do the killing?
We should let them fight it out since we are commanded to get rid of them not necessary to kill them personally.
“Don’t deprive someone of opportunity to fulfill a Mitzwo Asseh deOrraisso.” A Jew may have that responsibility. I don’t believe a non-Jew has it.
Actually even a Jew doesnt have such a responsibility. If im buying the last esrog in front of you i will not be responsible to share it with you.
“If an Amaleki wants to fulfill Hashem’s will then he’s probably not an Amaleki.” That assumes that an Amaleki has no bechira, which, I believe, is false.
Obviously Amalek has a bechira. I think Sam wanted to say… if Amalek wants to do Hashems will and accepts 7 mitzvahs then we dont consider him as Amalek anymore and we dont have a mitzvah to kill him. I agree with Sam.
My favorite question is what do you do with a child whos mother is Jewish and father is an Amalek? (he is too young to accept the 7 mitzvahs)