Interesting.. Tho im still a bit confused as to how Ryuuzaki L. Lawliet survived.. Didnt we see him get buried in the manga?

That may have been a cover up. Empty coffins are buried for famous people all the time. L may have been "buried" to put Kira off his case.
L survived because his anme was written when Rem was already dieing.

Wouldnt Kira have seen the names, og what had been written of his name when he picked up the notebook from the sand?

Yes, L's name WAS written, but he wasn't killed because Rem was already dieing when she wrote his name; the dead can't kill.

I meant if Kira would have seen what had been written of his name? She must have reached something

Yes, Rem wrote L whole name.
And yes Light saw it.
But after becoming a Shinigami he started losing his memories. One of the first to go was L's name.