1. What was Molly Weasley spell against Bellatrix?
2. Did Mrs Weasley cast Avada Kedavra on Bellatrix?
3. Is there a difference between the killing spell Molly Weasley used on Bellatrix and the avada spell if they are different Why is one okay and not the other?

What was Molly Weasley spell against Bellatrix?

Get back! She is mine!” Bellatrix then started taunting Mrs Weasley over her son’s death, proceeding to laugh at Molly’s enraged response that the Death Eater “will never touch our children again!”. This provided an opening for Molly to strike Bellatrix with a curse that hit her straight in the heart, killing her.

Did Mrs Weasley cast Avada Kedavra on Bellatrix?

No, we don’t know what spell did Molly use to take down Bellatrix, but it certainly wasn’t Avada Kedavra. Whatever spell she used, it didn’t disintegrate Bellatrix either.

Is there a difference between the killing spell Molly Weasley used on Bellatrix and the avada spell if they are different Why is one okay and not the other?

Molly didn’t use that spell to get rid of Bellatrix, she used a combination of defensive spells that had the same effect. The Avada Kadavra spell is Dark magic designed to kill another. In order to use that spell a witch or wizard must have malice in their heart.