Let's start with this: There is no final answer to your questions. Philosophers of the last 100 years have not agreed on definitions of the words "fact" and "truth."
That said, let's get practical. A fact is something that can be externally observed and agreed on. Facts are pieces of information: This rock is red; the cat is on the mat.
Many things cannot be known factually. In the novel Emma, there are several characters who appear to be in love by all the facts presented - and it turns out not to be true at all! Emotion, purpose, literary and poetic power; and spiritual meaning are all aspects of truth, not facts.
What is truth? The most practical definition is that, if everyone who matters to a situation agrees on it, then it is true for everyone there. But that definition is flexible. Anyone may find out later that what we thought was true at the time is not true now, and possibly, never was.
Philosophers of science tend to propose that science does not discover truth, it merely finds things that are not factual. What has not yet been disproven is called a theory or a law. But science is always open to discovering that there is a better, more accurate, simply picture of the truth. So science declares nothing true. (If people understood this, there would be much less conflict between science and religion.)
Each religion and philosophy has its own take on Truth. In faiths that focus on God, we can say that Truth is what God knows to be true. Then we seek to learn what God knows, and to see the world as God sees the world.
In Buddhism and some Hinduism, Truth is known by two qualities. First, it is factual, not contrary to facts. Second, it is harmless. Acting on Truth eliminates suffering, and does not create it. For Truth is Love, and Love is Harmless.