I think an important distinction is that in pre-meditated violence, the violent party has had an opportunity to cool off from whatever it was that compelled them to violence, as well as a chance to think through their actions, but still decided to go through with it. This clearly shows malicious intention, and often times in such cases one could argue that a reasonable person would realize violence wasn't the best way to go about taking care of whatever situation it was. By comparison, with non-pre-meditated violence, spirits are often still running high. One could argue, depending on the case, that an average person would be compelled to violence in such situations. It's somewhat related to the concept of fighting words - there are certainly words that can be said and actions that can be done that incite violent action in a lot of people, and it can't be entirely surprising if violent action results from them. It isn't so much someone's character driving them to violence in that situation as their inherent characteristics as a human.
But of course there are many shades of gray in this distinction. Formaldehyde raises an excellent point. If someone does have a history of violence, it can certainly be argued when they commit another non-pre-meditated act that they have not tried to address their violence problems. And I don't think it's inherently unfair for them to be treated more harshly than someone without a history of violence, if only because it sends a message that they need to try to avoid such situations. If you've got 5 records of non-pre-meditated assault in 10 years, you need to start avoiding the situations that are leading to that.
You could also, in rarer occasions, make a case that even in pre-meditated violence, an average person may be compelled to it. This is a lot narrower of a window, but in cases where the violent person was abused or otherwise heavily controlled by others over a long period of time, it could be argued that many people would snap and perhaps act out on a violent plan they'd considered but not done in the past. But the person in this case would have to have already been under the influence of demonstrably "bad" people to really make this case.
As for the sub-questions, it depends. For murder, perhaps it should affect the severity of the sentence, but not significantly, unless the murder was not intentional (in which case, it would be manslaughter, I think?) - such as if it would have been assault, but by an unforeseen circumstance it became fatal. In that case, you could make a case that the aggressor was prodded to actions by fighting words or similar as may apply, and it would have been assault had not something happened (like a car unexpectedly coming quickly when the aggressor shoved the other person into the street). For something like that, there's a considerable difference between bad circumstances and intentionally shoving someone into a car's path. Another example could be shoving someone, and they slip on ice and die of severe head injury. If it's non-premeditated, it's quite plausibly accidental that the person died; if it's pre-meditated, the meditator had time to realize the potential consequences of their actions and there's less room for claiming it was just bad luck.
If the murder was intentional, even if it was not pre-meditated, the penalty should be severe, though perhaps somewhat less. But if the aggressor punches someone to death, they had time to realize that the person was beat up and stop before they died, and if they shoot someone, they have to be aware of the risk of someone dying (an exception being if self-defence was involved, which may apply). So I wouldn't make it too much less severe.
I don't think there should be any difference in cases of rape. Having a difference would signify that it is OK or less bad in some cases. And you can't really make a case that some unforeseen, uncontrollable circumstance escalated it beyond what was intended.
For assault, I think it does depend on whether it is pre-meditated. The "fighting words" case can certainly apply, and if something like that happens and someone gets beat up, it isn't entirely surprising. Whereas if someone decided to just go beat someone up in their front yard or at an event that they know the other person will be at, they are well aware of what they are doing and are asking for trouble. So I think there is a significant difference there, and the sentence (and potentially, whether there even is a sentence) should take that into account.
For question 4, see above, but I would say usually. In extreme cases, perhaps not, but usually, it does, since that malevolence must continue for a much longer period of time.
