What is the reaction mechanism(s) and product(s) for a reaction
between 2-oxoethanoic acid and cyclopentadiene?

I'll give you a hint.

It's a name reaction, pericyclic 6 pi electrons, but not in the
classical sense. Good luck with your homework.

What name reaction is? Can you give me further hint?

I'll give you a hint: Try using the old name for oxoethanoic acid when searching.

I don't even know the old name os 2-oxoethanoic acid. Please, if you
know the old name for 2-oxoethanoic acid, would you tell me?

It's glyoxylic acid, try it in a Google search together with cyclopentadiene.

(Look up old names in a reference-book like "The Merck Index", or
simply search for them using Google next time, you'll learn a lot
more: ://www.google.com/search?num=50&hl=en&lr=&ie=UTF-8&safe=off&q=oxoacetic+acid
)

4 + 2 pi electrons.  Two guys are named for it.  Very famous...

The recation you're looking for is a Diels-Alder reaction. 
This is a reaction between a diene and a dieneophile.
The dieneophile in this case being the 2-oxoethanoic acid.
Usually (of course) the dienephile will be a C=C bond, but in this
case the C=O bond acts as the dieneophile.

the product is therefore 

   C=C
  C   C
   O-C
      COOH

hope this helps!

Or for completeness with all H shown:

     HC=CH
   H2C   CH2
      O-CH
         COOH

Thank you mr. djred for providing another hint to get him started. 
Too bad it's not the whole answer.