I found nice references for your questions. From there I am taking the next information:

Nautiloids were probably important predators of trilobites. Trilobites certainly were important prey for larger creatures. At first these were large invertebrates, such as predatory worms, nautiloids, sea scorpions (eurypterids), crustaceans, and perhaps Anomalocaridids. When fishes developed and flourished in the Devonian, we can be sure that trilobites were hard pressed by these new predators. For more information, please take a look into the next link:trilobites_predators

For the second part of your question I found this information:
The majority of early trilobites are thought to have been predators of benthic invertebrates, such as worms, and Cambrian trilobites such as Olenoides), often bore expanded and spiny gnathobases. Fossilized trilobite trails sometimes stop when they intersect worm burrows (suggesting that the trilobite was hunting for worms, and stopped to eat when it found one in its burrow ). Presumably the worm was extracted, subdued and crushed or torn apart with the leg spines and strong gnathobases, then passed forward between the legs to the anterior mouth, where last processing was done against the hypos tome platform before ingestion. In crustaceans and insects, all of these functions are served by specialized anterior mouth parts on the head of the animal for processing food before ingestion. However, in trilobites, most of the processing occurred in the longitudinal medial groove between the limbs, with their repeated pairs of gnathobases, meaning that the "mouth parts" of a trilobite occupied the length of its under body, rather than being primarily anterior.

Another piece of inference on the predatory nature of early trilobites can be gained from looking at the relatives of trilobites. The sister-taxa of trilobites, such a Naraoids, also included predators. For more information, please take a look into the next link: trilobites_food.