Learn Italian: Camminiamo intorno al lago.

In Italian, the word for around in a physical sense is the phrase intorno a. Because lago (lake) is masculine and uses the definite article il, the preposition a combines with il to form the combined word al.

I've learned that circa means around. Could I use it here?

No, because they mean different things in Italian. You use intorno a for a physical space, like walking around a lake or sitting around a table. You use circa when you mean approximately, like saying around five o'clock (circa le cinque).

Could I use the verb passeggiamo here instead of camminiamo?

Yes, but it changes the feel of the sentence slightly. Camminare refers to the physical action of walking, often for exercise or to get somewhere. Passeggiare specifically means to take a leisurely stroll. If your walk around the lake is a relaxing stroll, passeggiamo is a perfect choice.