First Age Easterlings were known as Swarthy Men, and after the War of Wrath, the evil side of this men fled back into the East where their kinsfolk spread and lived. Are the Second Age and the Third Age Easterlings related to these Swarthy Men, or not?
Short summary: we can't say for certain they are not the same. Anything else is conjecture.
In the First Age, "Easterling" referred to Men that lived east of Beleriand; this would have included Eriador. In later Ages, it still refers to peoples from "the East", which is to say, further east than those lands settled by the Dunedain.
If there were any survivors among the Swarthy Men, they necessarily relocated to Eriador or further east after the War of Wrath. There is no information on what they did there, or how they mixed with groups of Men that never entered Beleriand.
The only thing we know about the various non-Dunedain groups is that the inhabitants of Rhovanion (the Woodsmen, the men of Dale, and the ancestors of the Rohirrim, for example) were thought to be descendants of Men related to the Edain that did not cross into Beleriand in the First Age. Nothing else is really known about the other groups.