Do spiders eat other spiders?

Depends on the species of spider. Cobweb building spiders, such as cellar spiders, generally eat smaller insects and other arthropods in their diet. And important exception would be the widows, which often eat roaches twice their size.

Orb weavers, also web building spiders, may choose larger pray than the cobweb spiders , such as wasps (Seen Argiope aurantia orb weavers eat wasps). Ground hunting spiders such as wolf spiders have a similar diet, but often choose larger prey. Large mygalomorphs such as tarantula's and trapdoor spiders will generally eat anything they can catch (Lizards, roaches, crickets), and often take long breaks from eating.

Hope this helps.

Yes but only some not all Black Widows get their name from the habit of eating their mates.

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