>> He doesn't choose<<
Beggin' your pardon, but He does. Israel was chosen over the other nations. Jacob was chosen over his older brother. Joseph was chosen among his brothers. Esther was chosen to be the right person "for a time such as this". The old testament prophets were chosen. The new testament apostles were chosen. David, Saul, Solomon, Paul, Mary, Noah - all were chosen and favored over others. God leaves nothing to any degree of "randomness".
Your verse selection is also take out of context. In this instance, Christ is pointing out that God is just to both the good and the evil, and as such, we are to love our enemies and not persecute them. It is a description of God's supreme authority over everyone.
>>Love loves everyone, even the sinner.<<
There are degrees of "love" that boil down to definitions. You love your wife differently than you love your children, and both differently than your neighbor. Everyone sins, and as such, we have all trespassed His law. His love for us who are in Christ is such that we don't receive the punishment that we're obviously due, because of Christ's attonement for the elect. The unsaved, most assuredly, receive the punishment they are due.
We all sin, but God's love for His people are what make the difference in how our sin is satisfied to Him.
>>if he or she rejects Him and chooses to stay and die in the darkness.<<
We are all born into darkness. Only by the grace of God through the regeneration by the Holy Spirit can we see our sin for the vile thing that it is. A regenerated heart hates sin and rejects it - and pursues righteousness. It's irresistable.
We are all dead in sin, and a dead man cannot "choose" life - it can only be given.
Does He force or does He offer? I would say the latter (Love does not impose itself.
Oh, yes He does choose -- to give us blesisngs and to let us accept or reject them. He does not make the choices for us, but He helps us if we ask (Love does not refuse). He also chose Adam and Eve, since you are making up a list! And even when they transgressed He offered them a chance to repent -- a choice to change their mind, to repent.
According to your theology -- He must have created Adam and Eve in order to tempt them to sin so He could fulfill His plan of our salvation! That is a strange Christian God indeed.
"We all sin, but God's love for His people are what make the difference in how our sin is satisfied to Him."
Satisfied to Him? Like I said earlier, you write of a God to be saved from, not by.
What, exactly, do you believe God's purpose was in creating us?