Does God get a fail in the love category?
It depends on what you mean by "love". If it is the general understanding, then "Yes"; if it is some weird definition of "love" hemmed about with exceptions and unlikely explanations, then "No."
Do you believe that God loves us?
Not in the same way that I love my family and dog. Apologists say what God does and then they call that "love".
God is also said to love us unconditionally. Does God love us unconditionally?
Who says that? I suspect it is deluded "fluffy-bunny, cafeteria Christians, who pick and choose the nice bits in the Bible, and who chant out this sort of garbage in a mindless manner. God does not
love us unconditionally! What sort of god would that be?2 Chronicles 15:13 Whosoever would not seek the LORD God of Israel should be put to death, whether small or great, whether man or woman.
John 15:6 "If a man abide not in me, he is cast forth as a branch, and is withered; and men gather them, and cast them into the fire, and they are burned."
2 Thessalonians 1:8 "In flaming fire taking vengeance on them that know not God, and that obey not the gospel of our Lord Jesus Christ:"
Also, those who work on the Sabbath, even collecting sticks, those women who try to tell men what to do, and a whole host of others are damned eternally. Keep to every one of His 623 commandments and you might, just might, experience some love after you are dead and there are no witnesses about.
Love and morals developed to enhance interaction and living within groups of people and perhaps other entities. God was alone and did not need to develop morals and could not love anyone because he was alone for untold millennia.
The fault here is that you have no idea what Christianity is saying, do you? God was not alone. He had created the Host of Heaven (inc. the Devil and Jesus) way before he made the Earth and the firmament and the little holes where the rain comes in, and the fountains of the deep and seas and Malaria and polio, and smallpox and cripples, etc.
Is God even able to love?
Yes but not "love" as we know it, Jim.