(1) Yes
(2) No (*), there is no 'objective' morality
(3) Huh? Agreed: the word 'spirituality' is a sock puppet
2- No, there can't be an 'objective' morality (OM) because there is no standard, no law-giver.
There only are distribution curves of decreasing degrees of agreement to any moral statement.
Let's take an extreme example; moral statement 1 (**): is it OK to murder an innocent child?
I hope absolutely 100% here would say it's wrong. So we would call it objective morality.
Except that it's not 100% and I can think of one bad and one good example.
Bad example: the deranged psychopath. He just won't see the objectivity of that morality.
But the much better -and classic- example: you are part of a small group of twenty persons of a hunted minority (let's say, Jews trying to cross to safety during WWII) and a small party of the hunters is walking near your group, not yet seeing you (here, a patrol of Waffen SS with machine guns). In the group, a baby starts crying as the hunters party approaches hearing distance and the baby can't be stopped from making sounds. What is the objective morality? Kill the baby to save the group? Will the baby's mother agree to that morality? The objectivity of even an apparently unassailable (**) proposition crumbles.
But (*), it's a bit like 'Free Will', it's a play on words because we must act as if there was an objective morality. In general terms, save extraordinary circumstances, we should all consider not murdering an innocent child 'objective' morality.
PS: theist apologists are very big on trying to establish there IS an objective morality. Then they proceed to say such objective morality couldn't be established by humans who differ on so many things, and conclude there has to be an objective law giver, whish -tadaa- is God.