Would people panic and freak out?
Yes. They've just been given proof that they are bound for unavoidable, permanent torment. You know that sooner or later you'll be force-fed your own guts and eaten alive by spider demons. And there's nothing you can do about it. It's literally the worst thing ever.
Would murderers become the most heinous criminals of all? (Not that they weren't but you get my drift, if you kill someone you are also consigning them to hell for all eternity.)
Aside from God himself, yes.
Would having children be seen as reprehensible?
I don't think so. It's possible that having kids will be seen as a good thing since it's one of the few things that can give us hope that someone, eventually, will figure out a way to fix things.
Would nations go to war anymore knowing the price their soldiers pay and even if they did would their soldiers fight?
You would think so, but I think politicians are sufficiently bastardly to think ruthlessly killing the enemy outright will protect their own soldiers rather than ceasing armed conflict. I would envisage a drawing back of troops, though, perhaps everyone being defensive.
Would suicide bombing cease over night?
I doubt it, religion would just fracture and people would claim God is looking after them as always.
Has religion lost its meaning now that no matter what you say or do you are damned?
It will continue to offer false hope and merely deny the divinity of the entity that appeared.
Perhaps I'm missing a much more basic reaction. Would humanity simply blow itself up in a fit of suicidal insanity at the prospects facing us?
Or would humanity actually go on, perhaps drop significantly in population but still go on. And on a moral level is it per se evil to have children if you know they will eventually suffer for all eternity?
Humanity would soldier on in a futile attempt to fix the problem. I imagine the vast majority of world resources would go into investigating the nature of the paranormal, and whatever we can do to extend life at all costs. Immortality just became the number one goal.
We would rationalise the doomed nature of humankind, we would come up with religions that lie just as much as the current ones and give false hope against the god that appeared. It would be morally evil to have children for a vain hope of salvation, but due to the way our lives revolve around breeding and the hope it would give us, I wouldn't really blame people for doing it.
Also, iron chariots don't stop God. A couple of pages after Judges 1 (which specifies the limitations of the men of Judah, rather than God) God beats a king with similar armaments.