In Genesis,..when it reads she(Eve) bore again,is that referring to that Able being born 1st was actually Adam son-but then she gave birth again(implying right after Ables birth,...meaning they were twins of some sort but Cain not being Adams son,...instead implying that Cain was Lucifers actual biological son?
In Genesis 4:1-2, we see that Cain was born first, not Abel as you said.
Now Adam knew Eve his wife, and she conceived and bore Cain, saying, “I have gotten a man with the help of the Lord.” And again, she bore his brother Abel.
The timing of these events is not mentioned, but it is reasonable to assume that at least 9 months passed from Cain's birth to Abel's birth. There is no reason to think that either Cain or Abel were not Adam's sons.