When I booked with Disney, they said that we would get EMH every morning (we're there Sun to Tues), but from what I've read on here, it's not everyday!
There are some days in the coming months it is not offered at all. If you check the official website it tells you what days it is on. It is on all weekends though.
Also (sorry, lots of Qs!), we're stopping overnight in a holiday inn the night before so that we can have a whole day in the park, will we be able to check in and leave the car in the carpark in time for EMH?
Yes, you will. I doubt your room will be ready that early so you can either leave your luggage in your car or put it in left luggage at your hotel, whatever you prefer.