On the working from home point, I would assume you cannot assume you could just ask them about balancing work/get their opinion, although it isn't necessarily impossible that you could speak to them too (e.g. it is not that they are on leave). Therefore you might not be able to get their opinion and therefore how would you make a decision/what decision would you make if you haven't got the person around to just ask a quick question by walking up to them. I'd also consider that you are not limited to working in the office, and therefore your ability to work is something you could do around your appointment.
Discussing and agreeing deadlines for work is a key part of the job - you can't do everything and there is a team of people to work with when you have got important commitments. But if you have just received emails (and several of them) it's unlikely the expectation would be that you would do all that work that evening.
I'd also pick out that you are still waiting for the information from the third party - there is no definition as to when that information could come through. So think about how you will manage that ahead of the 10.00am meeting.