Is unhappiness/happiness something more then negative/positive feeling?

I rephrase your question as "can I plan to improve the current situation in the future, without experiencing any aversion to, or dissatisfaction with, the status quo? And does this mean that I'm happy?"

Taking the Buddha himself as the example, did he teach the Dhamma because he was dissatisfied with the status quo of the masses?

No. He simply taught, in various degrees, out of compassion and knew that it will be more helpful to some and less helpful to others.

“Well, sir, why exactly do you teach some people thoroughly and others less thoroughly?”

“Well then, chief, I’ll ask you about this in return, and you can answer as you like. What do you think? Suppose a farmer has three fields: one’s good, one’s average, and one’s poor—bad ground of sand and salt. What do you think? When that farmer wants to plant seeds, where would he plant them first: the good field, the average one, or the poor one?”

“Sir, he’d plant them first in the good field, then the average, then he may or may not plant seed in the poor field. Why is that? Because at least it can be fodder for the cattle.”

“To me, the monks and nuns are like the good field. I teach them the Dhamma that’s good in the beginning, good in the middle, and good in the end, meaningful and well-phrased. And I reveal a spiritual practice that’s entirely full and pure. Why is that? Because they live with me as their island, protection, shelter, and refuge.

To me, the laymen and laywomen are like the average field. I also teach them the Dhamma that’s good in the beginning, good in the middle, and good in the end, meaningful and well-phrased. And I reveal a spiritual practice that’s entirely full and pure. Why is that? Because they live with me as their island, protection, shelter, and refuge.

To me, the ascetics, brahmins, and wanderers who follow other paths are like the poor field, the bad ground of sand and salt. I also teach them the Dhamma that’s good in the beginning, good in the middle, and good in the end, meaningful and well-phrased. And I reveal a spiritual practice that’s entirely full and pure. Why is that? Hopefully they might understand even a single sentence, which would be for their lasting welfare and happiness.
SN 42.7

The Buddha also was not concerned with how many people he would save or not save, from suffering.

So what exactly has been declared by Master Gotama?”

“Uttiya, I teach my disciples from my own insight in order to purify sentient beings, to get past sorrow and crying, to make an end of pain and sadness, to end the cycle of suffering, and to realize extinguishment.”

“But when Master Gotama teaches in this way, is the whole world saved, or half, or a third?” But when he said this, the Buddha kept silent.

Then Venerable Ānanda thought, “The wanderer Uttiya must not get the harmful misconception: ‘When the ascetic Gotama was asked this all-important question he falters without answering. He just can’t do it!’ That would be for his lasting harm and suffering.”

Then Ānanda said to the wanderer Uttiya, “Well then, Reverend Uttiya, I shall give you a simile. For by means of a simile some sensible people understand the meaning of what is said. Suppose there was a king’s frontier citadel with fortified embankments, ramparts, and arches, and a single gate. And it has a gatekeeper who is astute, competent, and clever. He keeps strangers out and lets known people in. As he walks around the patrol path, he doesn’t see a hole or cleft in the wall, not even one big enough for a cat to slip out. He doesn’t know how many creatures enter or leave the citadel. But he does know that whatever sizable creatures enter or leave the citadel, all of them do so via this gate.

In the same way, it’s not the Realized One’s concern whether the whole world is saved by this, or half, or a third. But the Realized One knows that whoever is saved from the world—whether in the past, the future, or the present—all have given up the five hindrances, corruptions of the heart that weaken wisdom. They have firmly established their mind in the four kinds of mindfulness meditation. And they have truly developed the seven awakening factors. That’s how they’re saved from the world, in the past, future, or present. Uttiya, you were just asking the Buddha the same question as before in a different way. That’s why he didn’t answer.”
AN 10.95

If anyone doesn't bother to listen and follow his teachings, the Buddha simply gave up teaching him or her and moved on.

“Sir, what do you do with a person in training who doesn’t follow these forms of training?”

“In that case, Kesi, I kill them.”

“Sir, it’s not appropriate for the Buddha to kill living creatures. And yet you say you kill them.”

“It’s true, Kesi, it’s not appropriate for a Realized One to kill living creatures. But when a person in training doesn’t follow any of these forms of training, the Realized One doesn’t think they’re worth advising or instructing, and neither do their sensible spiritual companions. For it is killing in the training of the Noble One when the Realized One doesn’t think they’re worth advising or instructing, and neither do their sensible spiritual companions.”
AN 4.111