I must admit I have never heard of that definition of salvation before. I would agree that "achieve eternal happiness" is incident to salvation.
Anyway, as to whether we can be sure, I would just look to God's promises to us for certainty. Among the many:
John 10:27-29 "27 My sheep listen to my voice; I know them, and they follow me. 28 I give them eternal life, and they shall never perish; no one can snatch them out of my hand. 29 My Father, who has given them to me, is greater than all; no one can snatch them out of my Father's hand.
Phil. 1:6 "...being confident of this, that he who began a good work in you will carry it on to completion until the day of Christ Jesus.
We are told to be confident that He will not leave us, or allow us to fail by thwarting His good work, once (even "initial") true salvation is achieved. We are told that no power, not even our own will, can snatch us from His hand.
It sounds like the Buddhist and Hindu definition of salvation; i.e., Nirvana. Not a state of eternal presence with God, but a state of self fulfillment and personal bliss.
Scriptures mention "being saved" as a past, a present, or a future act. Thus, in one sense, we are "saved" when we are baptised, being saved during sanctification, and will be saved when we enter heaven. Here is where sometimes we talk past each other. Often times, Protestants refer to the one past event, while Catholics are refering to the future event. Thus, the misunderstandings.
Anyway, as to whether we can be sure, I would just look to God's promises to us for certainty.
The promises that you mention are rules of thumb for the general person. Since I am human, with a warped sense of self, I would be deluding myself to think that I can fully know where I stand with God. We have a tendency to overlook our faults and exaggerate ourselves in God's (and others) eyes.
For example, John 10 - how do I, ME, Joe, know that I am one of the sheep who will hear Jesus' voice five years from now? I know people who seemed to be pretty good Christians - but later - fell away. Thus, we must persevere in Christ. I don't know what will happen in the future. NOW, I can have a pretty good idea (but not certain). But the future? No one can snatch me out of Christ's hand, but I can willingly leave the flock.
On Phillipians, we can be sure God will not abandon us. But will we abandon Him? I don't know for sure. I work out my salvation in fear and trembling, running the race to the end for fear of being disqualified from the prize. To say otherwise is called presumption - which Paul says "those who think they stand securely, beware lest you fall". As long as we abide in Christ, we will be saved. Bottom line.
We are told that no power, not even our own will, can snatch us from His hand.
I don't see that. Christ (and Paul in Romans 8) is refering to an external force that pries us out of God's grasp. If God respects the freedom of man - if God awaits our response to the choice He lays before us, then there must be a possibility that we will fall. Clearly, this means that God knew we would turn away. Does God force us to do good or evil?
regards