These answers can vary depending on the time of year you go. At off-peak times, Wishes and Spectro may be shown around 7 or 8pm, and at peak times Spectro may be shown twice with Wishes shown around 11pm. Spectro is not an every night thing so you would need to check out the entertainment schedule but Wishes usually is, unless they have a hard ticket event like the halloween party going on.
Spectro and Wishes are not determined by the EMH schedule and Wishes should happen nightly. Spectro may be affected by EMH but I'm not sure.
Illuminations is every night at 9pm, regardless of the time of year (maybe new years is the one exception) or EMH.
Parks with evening EMH will close 3 hours after the regular time. So, Epcot closes every night at 9pm. On EMH night, the main attractions will close at 12am. MK will probably close at 10pm on an off-peak night and maybe 2am on a peak night (summer/Xmas week) but MK schedule can vary a bit so its always worth checking out the park hours pages here to make sure.
Hope this has helped,
Claire