Is the attempt to understand others a form of value judgement? In a recent conversation and in an attempt to understand others, i found myself not able often understand the actions or behaviors of others to leading to a sense of mind numbness. 

If i am not able to understand the actions of others, i find that i am in a state of not understanding and my mind/brain attempts to make sense of it. 

This can be extremely vicious since i am unable to let go and i often find myself in an infinite loop of sorts which in many situations is very demotivating, depressing and saddening.


Should i not attempt to understand the behaviors of others especially if they have cause harm be it mental, physical or emotional?
If i do not understand their actions, how does one approach the individual?
If i did understand, is it a form of value judgement?
If i were to abandon the choice to understand, is it a form of value judgement?


Examples - This are real-world situations i have faced


For example, if i were approached by an individual who had
traumatized another and my inability to reconcile their behavior made
it highly saddening as to why one would hurt another?
Another example is when i find others taking a short term view of
situations or simply not working with others in a cohesive manner
(looking after their own interests).
The unwillingness to help when help is sought or to forsake other priorities when attention is needed in other areas


I am unsure what the Buddha would do in situations such as these. If he were approached by a murderer for example, what would the Buddha's do, say, not say, etc?
This is one of the interesting aspects of Buddhism, that in its ideal form it doesn't allow prejudice (valid or otherwise) to interfere with the teaching. The Buddha taught people of all sorts, good and bad.

&quot;Brethren, the omniscient Buddha whose wisdom is vast, ready, swift, sharp, crushing heretical doctrines, after having converted, by the power of his own knowledge, the Brahmins Kūṭadanta and the rest, the ascetics Sabhiya and the rest, the thieves Aṅgulimāla &amp;c., the yakkhas Āḷavaka &amp;c., the gods Sakka and the rest, and the Brahmins Baka &amp;c., made them humble, and ordained a vast multitude as ascetics and established them in the fruition of the paths of sanctification.&quot;
-- Jāt 542 (Cowell, trans)

The only distinction he seems to have made when deciding who to teach is between worthwhile and pointless.

Now the Blessed One thought: 'To whom shall I preach the doctrine first? Who will understand this doctrine easily?'
Mv 1.6 (Rhys-Davids, trans)

Since Buddhism teaches the overcoming of partiality, the first thing one should accomplish when trying to come to terms with other people's behaviour is to free oneself from sadness or anger at the bad deeds of others.

Whether that venerable one dwells in the Sangha or alone, while some there are well behaved and some are ill behaved and some there teach a group, while some here are seen concerned about material things and some are unsullied by material things, still that venerable one does not despise anyone because of that.
-- MN 47 (Bodhi, trans)

Having said and quoted all this, on to your questions:
1. Should i not attempt to understand the behaviors of others especially if they have cause harm be it mental, physical or emotional?
There is no reason to single out such behaviours. But the question of whether one should ever attempt to understand the behaviours of others is more interesting. The goal of Buddhism is ostensibly the attainment of freedom from suffering. Insofar as understanding the behaviours of others leads to freedom from suffering, it should be pursued.
Certainly, understanding others is considered useful in understanding oneself; it is also useful in helping others to understand themselves, as you can then provide advice and point out (tactfully) facets the other person may be missing about their situation.
2. If i do not understand their actions, how does one approach the individual?
Buddhism doesn't recognize the existence of an individual in ultimate reality. Hence, taking the present for what it is. This helps immensely in interpersonal relations, as one need not bear grudges or prejudge others based on their past. Since beings are fluid and dynamic, the best way to approach others is with an open mind, ready to take them at face value in the present moment.
3. If i did understand, is it a form of value judgement?
In Buddhism, we tend to think more in terms of partiality than judgement. Judging whether something is good or evil can be wisdom based; partiality is always based on delusion (or more directly, one of four: desire, anger, delusion, or fear - the four agati). So, understanding whether someone's actions are good or bad is useful; liking or disliking them is harmful.
4. If i were to abandon the choice to understand, is it a form of value judgement?
I guess you mean is it a form of e.g. aversion if you reject the impulse to understand others? If so, then for sure it can be; it all depends on one's mindset. In general, the Buddha was critical of those who refuse to help others:

‘In the same way, Lohicca, if anyone should say: “Suppose an ascetic or Brahmin were to discover some good doctrine and thought he ought not to declare it to anyone else, for what can one man do for another?” he would be a source of danger to those young men of good family who, following the Dhamma and discipline taught by the Tathāgata, attain to such excellent distinction as to realise the fruit of Stream-Entry, of Once-Returning, of Non-Returning, of Arahantship — and to all who ripen the seeds of a rebirth in the deva-world. Being a source of danger to them, he is uncompassionate, and his heart is grounded in hostility, and that constitutes wrong view, which leads to ... hell or an animal rebirth.
-- DN 12 (Walshe, trans)

but this doesn't mean one need go out of one's way to try and figure others out, just that one should help others as appropriate. And of course, in order to help, one must understand.

One should first establish oneself in what is proper; then only should one instruct others. Thus the wise man will not be reproached.
-- Dhp 158 (Buddharakkhita, trans)

In summary, understand others is useful in that it gives the potential to help oneself and others. It is partiality that is problematic, as well as obsession with others to the extent that one forgets oneself.