Ask them to check if their reservation shows that they are eligible for dubai connect. They could use it, get a complimentary visa (if the need it) and drop off their luggage at the Le Meridien Hotel, have a shower/freshen up and then go do their sightseeing. There are plenty of inexpensive hotels near the airport that they can go to. If they do Dubai Connect they will have to check out about 3 to 4 hours before their flight anyway and the shuttle to the airport takes about 7-10 min so it would be perfectly in the midnight time frame.

Burj Khalifa is best at sundown-ish, you get a great day into night view and you can watch the dubai fountain at a time where the light show is better.

I like the madinat as a place to hang out and have drinks/food and do a bit of shopping if they want. Better than a mall in my opinion as there is outdoor seating and in April it shouldn't be too bad (there's also the malls and the souk for shopping). It's also right by the Burj Al Arab and Atlantis if that's something they're interested in.

As for dress code, shorts are perfectly fine for men but I would be a little cautious with the length of shorts for women. My sisters usually go with knee length dresses or 3/4 just to be safe. I know a lot of people will say it's not necessary but why risk the bad mood of the morality police...