Is there any way to find a specific player who doesn't show up on your battle tab and is off the news tab because its been over 2 days?

No

Although check your planets if you think you may have one of there on scan you can find what legion there in that way
Post here on the forums maybe somebody knows where the player is and can help you, the higher they are the more likely well known they are and thus easier to find

So there is no way to find someone and pvp later in the game after you have leveled up? I actually know what legion he/she is in but that doesn't help me to engage with him. (or does it? )

Nope. You can only engage him if
1) he's on your bt
2) someone alerts him within your legion
3) he's top 10 on kills leader board

http://galaxylegion.com/forum/viewtopic.php?f=3&t=5307

My first ever forum topic lol

Good thread Sparky. Very useful, thanks