Learn Dutch: Zij staan het standbeeld te fotograferen. - They are standing photographing the statue.

Both mean that the action is happening right now. The aan het + infinitive structure is a general continuous form. However, Dutch speakers love to be specific about body posture. Since the people are standing while taking pictures, it is very natural to use staan te + infinitive instead.

Why is het standbeeld sandwiched between the verbs?

This is the classic Dutch verb frame. The conjugated posture verb (staan) takes the second position in the sentence, while the remaining verb parts (te fotograferen) are pushed to the very end. The direct object (het standbeeld) has to go in the middle.

Does the word standbeeld have anything to do with the verb staan?

Yes, it does! Beeld means image or sculpture, and stand comes from the verb staan (to stand). So een standbeeld is quite literally a standing sculpture.

Could I use ze instead of zij in this sentence?

Yes, you can. Ze is the unstressed word for they and is extremely common in everyday speech. Using zij instead tells us that the speaker is putting a little extra emphasis on exactly who is taking the photos.