EMH is only available to onsite guests. If you are not staying at one of the three Disney hotels, you can't use it. If you are an onsite guest, you can use it every day you're staying onsite including check in and check out days. Meanwhile people with certain tickets will be given one day of MM, regardless of where they are staying.
EMH happens at both parks (usually alternating days), but MM only happens at DL. MM at DL happens on the same days as EMH at DL.
So basically, of you are staying onsite you can use early entry as much as you want at whichever park offers it that day. If you are stayong offsite but your ticket gives you MM, you can use early entry only once at DL on certain days.
I think the usualy schedule is DL EMH/MM on Tue, Thur, Sat and DCA EMH on Mon, Wed, Fri, Sun. This can change, but I think they only really change it during very busy times and special events.