That is true, from God's point of view. I do not necessarily agree that WE know if we are saved (defined as "achieve eternal happiness") without ANY doubt. WE don't know if our names have been blotted out of the book of Life (or will be). But we can have a pretty good idea where we stand if we examine ourselves and see whether we are obeying the Commandments. 1 John is a very good epistle that covers how we can know we are saved - because (as you mention) we can only do good IF we abide in Christ. Thus, if we have good inner dispositions, loving others for the sake of loving them (not to earn something), we can rest assured that Christ is somehow abiding in us to a degree (since we cannot do that ourselves).
God will not allow the truly saved to ever be lost.
Yes, but am I of you or the "truly saved"? Paul in 1 Cor 6 tells us that certain Christians will not inherit the Kingdom of Heaven. Although by habit, we can rest assured that we are likely in Christ as we grow in virtue, that we can have "moral" assurance of salvation, even Paul continued to run the race LEST HE BE DISQUALIFIED. As you know, you get NOTHING for being disqualified from the prize of eternal life...
I do focus on God's love for me, and I love Him back through the ability to do so, which He gave me.
Very good. Again, 1 John tells us to love in deed, not in words. Deeds of love are demanded of us - not to earn anything, of course, but because it shows our response to Christ and His work within us. "Of the greatest of these is love" says Paul.
Regards
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.