It is shown that Pokemon eat fruit, PokeBlocks or some random eatables. However, I have never seen a Pokemon being eaten by another Pokemon. Also, their trainers don't seem to eat meat. As there are only Pokemon in that world, eating fish would be equivalent to eating a Magikarp or other fish Pokemon.
Horray for Bulbapedia!
The most commonly referenced mention of Pokemon eating other Pokemon is the entry about Pidgeot.
"When they hunt, Pidgeot fly on the surface of the water at top speed to catch unsuspecting Fish element prey like Magikarp."
It is also referenced in Shipwreck, where Meowth attempted to eat James' Magikarp.
Farfetch'd also has an entry about how delicious it is.
The general consensus from my research seems to be that, while pokemon are likely eaten by other pokemon and occasionally humans, it is rarely if ever portrayed because Pokemon is aimed towards a child audience.
It should also be noted that normal animals exist in pokemon. There are multiple references to them, although they are rare.
In both Raichu and Gastly's FireRed entries, Indian elephants are mentioned.
In several of Bellsprout's Pokédex entries, Bellsprout is said to prey on insects.
Victreebel is mentioned to use the Sweet Aroma of its honey to lure prey such as bugs, as well as large animals.
Horsea is said to prey on bugs in several of its Pokédex entries. Some entries also mention that Horsea uses coral as an anchor to avoid being washed away, as well as for shade to build its nest in.
Lickitung's Red, Blue, and LeafGreen Pokédex entries mention that it can extend its tongue like a chameleon.
The Pokemon Alpha Sapphire Pokedex entry for Wurmple states:
Wurmple is targeted by Swellow as prey. This Pokémon will try to resist by pointing the spikes on its rear at the attacking predator. It will weaken the foe by leaking poison from the spikes.
And the entry in Pokemon X:
It loves to eat leaves. If it is attacked by a Starly, it will defend itself with its spiked rear.
These two entries show us how Wurmple is targeted as prey by Swellow and by Starly.
While Pokemon is targeted a younger audience and darker subjects like death are almost always avoided, we can conlude that the pokemon universe is not too different from our own in that pokemon, like animals, eat other pokemon.