So for my Department, it really should be a "minimum" of 40%, however a lot is down to managerial/head of unit discretion; as an LM I do take into account differing circumstances - some in my team prefer being in the office for the social interaction (which I get), some don't like it, like I say I'm much more productive at home, and trains/strikes can make the commute an absolute bl**dy nightmare. If you're worried, have a chat with your manager.
In terms of vetting - be honest. They know the truth already, they're just looking to make sure you are being truthful. Depending on the level of vetting, I wouldn't imagine it would cause a problem, but better to be safe than sorry IMO.
Also, if you haven't already, reach out to the recruiting line manager, have a chat with them, and get to grips with what the role is really about. CS job adverts are quite limited I find, and also when you get to interview you've already got an idea of what you're stepping into. Also, ask about any training available; for example if it's a policy based role, would you be expected to draft submissions for ministers, respond to correspondence, draft guidance?
Ask about career progression, however don't be surprised if the response is "it's your responsibility". As a manager, we do everything we can to help develop you, but at the end of the day if you want promotion, nobody else is going to do it for you.
Hope that's helpful!