(T- total depravity)
D 48. God has created a good world.
D 58. Our first parents, before the Fall, were endowed with sanctifying grace.
D 61. Through the sin our first parents lost sanctifying grace and provoked the anger and the indignation of God.
Total depravity is not dealing with the world God created specifically, but with the condition of all mankind. The total effect it had on all Adam's progeny. It is not dealing with sanctifying grace, but the radical and total effect the fall had on us in separating us from God. I suspect your religion teaches total depravity in the sense that the depravity affects every part of us. It differs in the rest of the doctrines of grace in TULIP. Since that is probably the case concerning the T, you should be able to answer the question in your own words, what the T means, and whether or not Jesus taught it and the ULIP.
Heb 4:15 Christ was sinless
D 89. Christ was free from all sin, from original sin as well as from all personal sin.
This is true, but it has nothing to do with TULIP or total depravity.
D 103. Mary was conceived without stain of Original sin.
(U- unconditional election)
The TULIP has nothing to do with Mary, and certainly not with unconditional election. And you attributed to Mary a condition upon which she was elected, and called it unconditional. The rest of what you categorize as unconditional election, either as an agreement or a refutation, I cannot tell and you do not say, are quotes from Catholic dogma. None of which has a thing to do with unconditional election, and do not answer the question of whether Jesus taught it. That would require a presentation of what Jesus taught, not a Catholic interpretation. And as this is not a Catholic thread, their interpretations should no be considered actually answering any question. You should be able to do that yourself, without reference to them---even if you come up with the same conclusion. Can you do that?
(L- limited atonement)
Jn 3:16 the whole world
Jn 1:29 the whole world
2 cor 5:19 reconciled the world
1 Jn 2:2 propitiation of the whole world
D 96. Christ did not die for the predestined only.
So---the whole world in those passages means every person without exception? Then you use another Catholic quote (D 96) that skips 500 steps before offering its conclusion and changes the conversation from the meaning of limited atonement and whether or not Jesus taught it, to something else entirely. The predestination issue belongs in the discussion of unconditional election. And when you were in the "U", you never bothered with that but started discussing Mary.
D 122. The Human Will remains free under the influence of efficacious grace, which is not
irresistible.
That is Catholic dogma and it is also a contradiction within itself. If the grace of God is efficacious it cannot be, because it will not be, resisted.
(P- perseverance of the saints)
Perseverance requires God’s grace / help requiring prayer
Matt 7:7 Matt 26:41
D 113. Without the special help of God the justified cannot persevere to the end in justification.
D 114. The justified person is not able for his whole life long to avoid all sins, even venial sins, without the special privilege of the grace of God.
Can you say that in your own words, finding its verification in the words of Scripture, and without the influence of Catholic dogma telling you what something means? I already know that they teach they are the only ones who can distribute this "special help of God", which turns the special help of God into the special help of men and traditions of men. Do you see how it is impossible in and of yourself for you to think outside of what has been indoctrinated into you? And as I said, this is not a Catholic thread, so Catholic dogma will never be a valid point of reference in address the OP question.
Did Jesus teach perseverance of the saints? (Here I must pause to give that word "saints" its biblical definition and not the Catholic one.) "Saints" in the Bible, and especially in the epistles, means believers. Those who believe the person and work of Christ and have put their faith and trust in Him---for everything necessary for salvation. The apostles in their letters frequently call those they are writing to "saints."
The question is quite easy to answer, and though there are many such examples in Jesus' teaching, this one, all by itself, will seal the deal. John 6:35-40.
Jesus said to them, "I am the bread of life; whoever comes to e shall not hunger, and whoever believes in me shall never thirst. But I said to you that you have seen me and yet do not believe. All that the Father gives me will come to me, and whoever comes to me I will never cast out. For I have come down from heaven, not to do my own will but the will of him who sent me. And this is the will of my Father, that everyone who looks on the Son and believes in him should have eternal life, and I will raise him up on the last day."
All who are in Christ through faith, have been placed there by God (given to Him), and they
will persevere because God Himself preserves them. He does not need our help to do this. He does not need baptisms, or transubstantiation, or penance paid, or earthly priests, or religion, or anything else, to do this. We live and move and have our being in Him. He leads us in paths of righteousness, directs our footsteps, makes our paths straight before us. He Himself, teaches us righteousness form His word and writes it upon our hearts.
The answer to the OP question, did Jesus teach TULIP is yes. He teaches the entire thing in that one passage quoted in John 6. And of course, that is not the only place.
See how easy that was?