As we are required to love our enemies, may we not safely infer that God loves His enemies? (Matt. 5:44)
As we are required to worship God, may we safely infer that God worships us? Of course not! Man is man and God is God. He loved us while we were his enemies, but this does not imply that he loves all of his enemies.
If God loves His enemies, will He punish them more than will be for their good?
False premise.
Would endless punishment be for the good of any being?
Of course not. The purpose of endless punishment is quite the opposite. In fact, Hell for any length of time is not an act of love, which summarily disproves the premise that God loves everyone, which is the underlying premise of the OP.
As God loves His friends, if He loves His enemies also, are not all mankind the objects of His love?
Only if he loves all of his enemies. God loves his enemies, but is there any reason to think that he loves all of his enemies?
If God loves those only who love Him, what better is He than the sinner? (Luke 6:32-33)
God doesn't sin, ever. That makes him better than the sinner. He's also God, which makes him better at any rate.
As "love thinketh no evil," can God design the ultimate evil of a single soul? (1 Cor. 13:5)
Hell is no accident. It didn't make itself.
As "love worketh no ill," can God inflict, or cause, or allow to be inflicted, an endless ill? (Rom. 13:10)
Endless or not, can love burn someone in a furnace? No.
As we are forbidden to be overcome by evil, can we safely suppose that God will be overcome by evil? (Rom. 12:21)
God is not overcome by anything, but according to Isaiah 45:7 God is capable of such things, like it or not.
Would not the infliction of endless punishment prove that God HAD been overcome by evil?
It would prove that God could inflict evil. It would say nothing about being overcome by it.
If man does wrong in returning evil for evil, would not God do wrong if He was to do the same?
A man slips and falls from a cliff, and God repays carelessness with evil. God metes evil for all kinds of reasons, for his own divine purposes. If he repays evil for evil it would be a more obviously noble reason than most other causes by which a person meets his doom. He has his divine reasons for all that he does.
Would not endless punishment be the return of evil for evil?
You bet.
As we are commanded "to overcome evil with good," may we not safely infer that God will do the same? (Rom. 12:21)
Are we gods?
Would the infliction of endless punishment be overcoming evil with good?
Endless or not, would torment be overcoming evil with good? Of course not! The endlessness of it is irrelevant to your point. (the endlessness of your line of questioning is a torment of its own)
If God hates the sinner, does the sinner do wrong in hating Him?
If the sinner hates God, then hasn't he merited God's hatred?
Is God a changeable being? (James 1:17)
No. That's why the punishment is endless.