What are the Tyranids running from?

The short answer is that nobody knows. The only thing that the fluff remarks on is that tyranids came from another galaxy and travelled through the intergalactic void. The Tyranids were running from a spieces superior to them.

When did the Tyranids come out?

Genestealers were introduced in the 1980s with Space Hulk, and later featured in Space Crusade, along with the short-lived Genestealer Magus. The first recognizable incarnation of Tyranid warriors appeared in Advanced Space Crusade in 1990, featuring biological weaponry such as boneswords and deathspitters.

Can tyranids be stopped?

If the tyranids are unstoppable, the orks are able to stop them. Both of them have infinite numbers, adaptability and psychic strength on their sides. The orks are even able to make the impossible possible. The tyranids are unstoppable in almost every sense of the word.

Did the old ones create the Tyranids?

The Old Ones created the Tyranids in a bid to stop the necrons from attacking them. The Hive Mind acts as a sort of seed bank for the DNA of various species, so they can be re-created at a later date.