As to the word manas, Thrangu Rinpoche said (paraphrasing):
All mental events—all thoughts, memories and anticipation of the future with all its emotions of happiness, sadness, excitement, and frustration takes place in the manas. It is the manas which differentiates and thinks and makes judgements about the perception. After the eye, ear, nose, tongue and tactile consciousness perceives an object, the manas judges the sensory perception with thoughts.
So the word manas here is used to drive home the idea that it is our mind -- in the sense of our outlook, our way of seeing and interpretation -- is what creates our reality.
In Tibetan Buddhism they have this notion called "pure perception" or "sacred outlook". It's a practice of seeing everything as expression of Buddha-Nature, without a taint.
When we see the world with pure perception, there are no enemies of ours, no aggression is provoked in us, no anger, no antipathy. The reality of our perception is pure. Then our reactions are pure, our karma is pure, and it results in peace.
But when our perception is tainted, we see a different reality, we are in a different world. So naturally this world provokes very different reactions in us, which lead to trouble.
It is our outlook that defines our reality, our actions, and its results.
This outlook is a state of mind.
This is what is meant here by the word manas.
If one speaks or acts out of an addled manas, dukkha follows him like the cart's wheel follows the ox's hoofprint.
If one speaks or acts out of a clear manas, sukha follows him like a shadow which never leaves.
Now, what exactly is addled/dirty manas and what is clear/pure manas?
Manas is not memory, it is only an organ of mental (inner, reflective) perception, thus supporting further interpretation and judgement - so how and why can it be dirty or clean?
Manas is exactly the part of mind where Upadana or Feeding occurs. Upadana is when we keep going over a certain idea or image or event, triggering our interpretation and emotional reaction again and again. As a result of this cyclic feeding, manas constantly keeps this idea "loaded", and presence of this idea affects or skews all new interpretation and judgment.
So the dirty manas or dirty outlook is what happens when we feed on negative, selfish, aggressive, divisive thoughts.
And the pure manas is when we don't feed, don't maintain these tainting dharmas (known as klesha or asava). As a result we see things yathabhuta - as they are. Seeing things as they are leads to right action, and right action leads to the ending of suffering and to harmony and peace.
This is why the subsequent verses of Dhammapada speak about (not) harboring offense and enmity, (not) dwelling on pleasant experiences, and eventually "vomiting all the asavas". These are examples of maintaining the dirty manas vs purifying it.