Learn Hardcore Latin: Mater in mortario allium et salem miscet, et pistillo parvo lente utitur. - Mother mixes garlic and salt in the mortar, and slowly uses a small pestle.

Latin word order is much freer than English word order, because the endings show how words function. Putting mater first gives it emphasis as the topic: Mother is the one doing these actions.

A very neutral English-style order might be something like:

Mater allium et salem in mortario miscet...

But the original sentence is perfectly natural Latin.

Why is in mortario in the ablative?

The preposition in can take either the ablative or the accusative, depending on the meaning.

in + ablative = in/on a place, showing location
in + accusative = into/onto a place, showing motion toward it

Here in mortario means in the mortar, so it shows location, not motion. That is why mortario is ablative.

What case is mortario, and what dictionary form would I look up?

Mortario is ablative singular.

Its dictionary form is mortarium, mortarii (neuter), meaning mortar.

So:

nominative singular: mortarium
ablative singular: mortario