No. True is simply a value we assign to a fact. The only constraint is that it is logically consistent with the remaining true facts.
Objectivity and fact are synonyms. Something that is objective has a truth value that is irrespective of anyone's perceptions or beliefs. A for absolute scale, it depends on what is being discussed-- if it is "existence", the scale is "exists" or "does not exist". Some things have scale with more shades inbetween.
Obviously, because such "facts" as you call them, comes from our (presumably) shared experience of the world. We call them facts because we can measure them, or deduct them from something we can measure. Of course, "facts" might change, either because our world changes, because our measurements changes, or because our deduction techniques changes. E.g, some times ago a number of religious beliefs (say, Jesus's revival) were considered facts, but today we know it not to be so.
But you are saying that evil is defined on a relative, subjective scale, and denying that there is any higher authority to which one could appeal for such an objective scale.
Of course. Doing otherwise would be insane.
The problem remains that you cannot call your own personal beliefs "true" while asserting that they are subjective. Either they are true, or they are not, and truth is NOT subjective.
You got it backwards. We do not instinctively know something is evil because the act is evil; rather an act is evil because we instinctively find it evil.
You can argue that that means that what is evil changes over time, and indeed, this is the case. E.g, the old testament has a lot of stories where one of the many gods therein ordered "his" people to do mass murder and genocides. Such an act might not have been considered evil then, but it certainly is now. I don't know why that bothers people.