Learn Turkish: Ormandayken katlanır bir tripod taşıyorum. - I carry a folding tripod while in the forest.

This is the aorist participle being used as an adjective. The verb stem is katlan- (to fold or be folded). By adding the aorist suffix -ır, it turns into an adjective describing something that can or usually does fold. So, katlanır bir tripod means a "folding tripod".

Why does it use katlanmak instead of the base verb katlamak?

The verb katlamak means "to fold something" (like folding clothes). katlanmak is the reflexive or passive form, meaning "to fold itself" or "to be folded." Since the tripod is designed to fold up, we use the katlan- stem to make the adjective.

How is -ken working in ormandayken if there is no verb attached to it?

The suffix -(y)ken means "while," and it can attach directly to nouns or adjectives! Here, it attaches to the locative word ormanda (in the forest). Because ormanda ends in a vowel, we need the buffer letter -y-, creating ormandayken (while in the forest).

Why is the verb taşıyorum (I am carrying) used instead of the aorist taşırım (I carry) for a habit?

In Turkish, the present continuous -yor tense is very commonly used to describe regular habits and routines, not just actions happening right now. While you could also say taşırım here, using taşıyorum sounds perfectly natural for a routine action.