Is it all about serial killers?

If you are referring to the series, no.

Now, the first dozen or so episodes of "Thriller" were just that, Thrillers. They involved basically situations involving murder, stalking, juvenile delinquency etc. somewhat like Alfred Hitchcock Presents (Of course with a different feel) One exception during this period was a Halloween episode called "The Purple Room" which was in the horror vain. Then, just before the new year came in (1961), the series took a rather dramatic turn toward the supernatural beginning with "The Cheaters" (Episode 15 which aired Dec. 27th 1960). This began the period of "Thriller" that most fans loved.

If you've only seen the very early episodes, these aren't very representative of the series.

Check out episodes like:

The Cheaters
The Purple Room
The Hungry Glass
Parasite Mansion
Terror in Teakwood
The Prisoner in the Mirror
The Grim Reaper
The Weird Taylor
Pigeons From Hell
A Wig For Miss Davore
Portrait Without a Face

This is pretty creepy stuff. And there are others.

I hope this helps.

Half the shows in the first season were crime /suspense stories mostly along the lines of Alfred Hitchcock presents but the rest were horror themed and I would recommend any of them since all the horror episodes are classic.

No, but young Rip Torn in The Purple Room is the spitting image of Ted Bundy, including speech and mannerisms.