Learn Dutch: Gaan jullie het interview vandaag opnemen? - Are you going to record the interview today?

Because this sentence uses two verbs: the helper verb gaan and the main verb opnemen. In Dutch, the helper verb takes the normal position (first place in a yes/no question like this), and the full infinitive verb gets pushed to the very end of the clause.

Since we are learning about the impersonal passive with er, could we change this to Er wordt het interview vandaag opgenomen?

No! The impersonal passive with er is used when there is no specific subject or direct object (like Er wordt gepraat for 'There is talking'). Because this sentence has a specific direct object (het interview), you cannot use the impersonal 'er'. A normal passive would just be Wordt het interview vandaag opgenomen? (Is the interview being recorded today?).

I thought time words like vandaag usually come early in the sentence. Why is it after het interview here?

When a direct object is a specific thing (using de, het, or a pronoun), it often comes before the time word. You could also say Gaan jullie vandaag het interview opnemen?, but putting the specific object first is very natural and common in Dutch.

Is opnemen a separable verb, and does it always mean 'to record'?

Yes, it is separable (op + nemen), though it stays together here because it is an infinitive at the end of the sentence. It means 'to record' for audio and video, but it can also mean 'to pick up' (a phone) or 'to admit' (someone to a hospital).