Learn Russian: Он запоминает быстро.

Reflexive verbs ending in -ся or -сь often show an action done to oneself or an action that happens on its own. Here, he is actively doing something to outside information (memorizing it). Because the action is directed outward rather than at himself, it uses the standard active verb form without -ся.

What is the dictionary form of запоминает and how is it conjugated here?

The infinitive (dictionary form) is запоминать (to memorize). It follows the very common First Conjugation. To make the form for он (he), you drop the -ть ending and add -ет, which gives us запоминает.

Why does быстро end in -о?

Быстро is an adverb meaning 'quickly,' used here to describe the verb (how he memorizes). In Russian, you create most adverbs from adjectives by replacing the adjective ending (like in быстрый - quick) with -о. Unlike adjectives, adverbs never change their endings to match gender or number.

Can I use запоминает to say 'he remembers' a fact from the past?

Not quite. Запоминать specifically means 'to memorize' or 'to commit to memory'—it is the process of learning. If you want to say 'he remembers' something he already knows, you would use a completely different verb: помнить, making the sentence Он помнит.