Learn Turkish: Ormandaki baykuşlar gece uçabilir. - The owls in the forest might fly at night.

You are right that the -(y)abil suffix combined with the aorist tense (here, -ir) is used for ability ("can fly"). However, Turkish uses this exact same structure to express probability or possibility ("might" or "may"). You have to rely on context to tell them apart. If we are stating a general fact about a species, it means "can". If we are guessing what these specific owls will do tonight, it means "might".

How does the word Ormandaki break down?

It is made of orman (forest) + -da (locative suffix: "in") + -ki. The -ki suffix acts as an adjective-maker here. It attaches to a location to describe a noun. So, ormandaki baykuşlar literally translates to "the in-the-forest owls".

Why doesn't gece have a locative suffix like gecede to mean "at night"?

In Turkish, common times of day like gece (night), sabah (morning), and akşam (evening) act directly as time adverbs. You don't need to add the locative suffix -da or -de to say "at night" or "in the morning"; just saying gece is enough.

Since the subject is baykuşlar (owls, plural), shouldn't the verb be uçabilirler?