Learn Turkish: Büyüteç çıkarılır bir mercek içeriyor. - The magnifying glass includes a removable lens.

Let's break it down: çıkarmak (to remove) + -ıl (passive suffix) + -ır (aorist suffix). The passive verb çıkarılmak means "to be removed". When you add the aorist suffix -ır to a verb to use it as an adjective, it often expresses a general capability, similar to the English suffix "-able". So, çıkarılır literally means "that which can be removed", or "removable".

Could I use the -An participle here and say çıkarılan instead of çıkarılır?

That would change the meaning. çıkarılan bir mercek means "a lens that is being removed" or "that was removed" (referring to a specific action happening to the lens). The aorist participle çıkarılır describes a built-in characteristic or capability of the lens: it is a "removable" lens, whether someone is actually taking it out right now or not.

What is the root of the word büyüteç (magnifying glass)?

It comes from the verb büyütmek, which means "to enlarge" or "to make bigger". The suffix -eç (or -aç) is attached to verbs to name a tool or instrument that performs that action. So, a büyüteç is literally an "enlarger".

Is the verb içeriyor (includes/contains) related to the word iç (inside)?

Exactly! The root noun iç means "inside" or "interior". By adding the verb-forming suffix -er, we get içermek, which means "to include" or "to contain" (literally, to hold inside).