is it important to understand peoples motivations before judging their actions?

Don't judge their actions, just take care if you need to care and if you care about such people you could at last try to understand their motivations too. In other cases just act or observe.

It depends on what your role in society is. More often than not, it is a very good idea, and fair idea to do so. However; there are those people who are put in positions of having to judge actions, and having to do it on a split seconds or having to do it without taking into considering any contributing factors to such actions. This is not to say that these people are the only ones to make these judgments. There are just others who will not allow motivations in to the picture when deciding specific judgments.

Yes. This is a very important principle in law. If I'm backing up in my driveway and accidentally run over your cat, this is a far different thing from hunting down your cat to run it over. The first action has no malice in it, while the second is full of malice. Malice is dangerous and society doesn't like it, especially the premeditated kind.

Accidents, even fatal ones, happen and must be taken as a part of life. If a driver has a heart attack and plows into an elderly couple, what are you going to do? Put the driver in prison because he had a heart attack? Not even the victims would want this. But if he were drunk, then he is culpable and should be punished.

It's good to understand what they were attempting to accomplish through their actions, especially if it was a failed attempt. But intentions aren't noteworthy in themselves, as in the instance of 'good intentions'. Someone might supposedly have good intentions, but if they don't thoroughly understand the situation and what their actions might do to worsen it, then it doesn't matter. What matters is that they chose to act out of ignorance and selfishness (because they felt they knew best), so it is the result of this which matters in that case. Saying that they intended this or that in a failed attempt should actually work against them, since it only serves to demonstrate how little they considered the situation before involving themselves in it.

yes, theres many ways to look at this, first question in awhile to make me think. if you look at it this way, imagine someone by them self unloading shopping into there house and a stranger comes to offer help *action, now what if he only helps to get into the house to have a look and see if shes there by herself. *motivation, so its very important to understand motivation in my opinion.

Yes, but it is also important that they still take responsibility for their actions.

If Billy was holding a loaded gun pointed in the direction of Muffin's head, and the gun goes off...but he loves Muffin, and didn't mean to kill her, is Muffin still dead? Yes.

Yes. Intention really does mean a lot. If something is meaningful to someone else, they will come from their POV but it doesn't mean they are doing anything wrong.

Example: Wishing "Merry Christmas" to a non-Christian. They are being kind.. . and that is what matters.

Yes but unfortunately we aren't mind-readers so really its hard to tell. Plus, if it affects someone who is totally innocent, then isn't the person who done the wrong action wrong anyways?

Yes can put a whole new light on the subject

Of course. Otherwise you stand to misinterpret their actions.