If a Jew spent his entire life doing terrible sins, would God still love him? For example, does God love Jesus or Jews who have caused similarly terrible damage? Please provide sources.
Well a word like "Love" when applied to Hashem has to be understood only as a metaphor. So, I would recast your question as: Does Hashem act toward sinners in a manner intended for us to experience as loving?
In the beraisa that is included volumes of Mishnah Pireqi Avos 6:1, Rabbi Meir lists some of the titles one gains by learning torah lishmah, Torah for its [proper] sake. Among them, three involving love -- "אָהוּב, אוֹהֵב אֶת הַמָּקוֹם, אוֹהֵב אֶת הַבְּרִיּוֹת -- beloved, loves the Omnipresent, loves human beings".
On that third one, "אוֹהֵב אֶת הַבְּרִיּוֹת -- loves human beings", the Tif'eres Yisrael writes:
לא לבד לאדם מיוחד, אלא אפילו אותן המקולקלין במדות, או בחטאים שאין לאוהבן רק מדהן בריות של הקב"ה:
Not only the distinguished person, but also those who are defective in Middos, or sinners who aren't to be lived except for their being creations of HQBH.
Even as we hate the fact that someone is a sinner, we are still supposed to love everyone G-d created, sinner or someone of higher aspirations, Jew or non-Jew.
Another example. Normally if one is faced with two mitzvos -- helping someone load their animal or helping someone unload their animal, a person must prioritize unloading. It is the more compassionate choice for the animals. But, if the person loading the animal is your enemy, then helping your enemy load the animal comes first. So as to "conquer your yeitzer hara".
Tosafos (Bava Metzia 32b) ask: Enemy? What kind of enemy? Aren't we prohibited to hate other Jews? He points out that we are supposed to feel hatred toward the sinner. So then why would we want to help the hated sinner so as to conquer our hatred of them?
They answer that not helping the person with their animal will inflame their hatred. And their hatred might inflame your hatred in response. While it is okay to hate a sinner for being a sinner, adding personal hatred on top of that is prohibited.
Now that's people. In addition, Hashem knows the sinner's background and motive, how the person got to this lowly state. This is what He expects us, with our ignorant about what goes on the minds of others -- to love every person (again, not just Jews) even while simultaneously feeling hatred toward those who sin.
I would expect so does He. Figuratively speaking.
'A baraita: The verse: “You are the sons to the Lord your God,” indicates that when you act like sons and cleave to the Holy One, Blessed be He, you are called sons, but when you do not act like sons you are not called sons. This is the statement of Rabbi Yehuda. Rabbi Meir says: Either way you are still called sons, as it is stated: “They are foolish sons” (Jeremiah 4:22). It also states: “Sons in whom there is no faithfulness” (Deuteronomy 32:20). And it states: “A seed of evildoers, sons who deal corruptly” (Isaiah 1:4). And it states: “And it shall come to pass that, instead of what was said to them: You are not My people, it shall be said to them: Sons of the living God” (Hosea 2:1). The Gemara asks: Why is it necessary to cite these additional proofs? If you would say: Granted, when they are foolish they are still called sons, as the verse states: “Foolish sons,” but when they do not have faithfulness they are not called sons; therefore, come and hear another verse. And that verse states: “Sons in whom there is no faithfulness.” יAnd if you would say: It is when they do not have faithfulness that they are called sons, as stated, but when they worship idols they are not called sons anymore; therefore, come and hear: And the verse states: “A seed of evildoers, sons who deal corruptly,” which alludes to the corruption of idol worship. And if you would say that although they are called “sons who deal corruptly,” they are no longer called full-fledged sons of God once they have sinned, come and hear: And the verse states: “And it shall come to pass that, instead of what was said to them: You are not My people, it shall be said to them: Sons of the living God.”'
There are different levels: very very different. But in the end we are all his children כביכול. How do you feel about your son? It depends on what he's done, of course. But in the end he is your son, and that means a lot.