1. From (recent) memory, you should get pyjamas and an amenity kit on EK30. I think I did.

2. The answer to this partly depends on whether your arriving and departing flights leave from the same part of Emirates' terminal at Dubai. Each concourse has its own First lounge. Travelling between concourses will eat into your stopover time. The answer is also a matter of what your preferences are. At the time your flight arrives from Heathrow food options will be more limited but breakfast should be available, with waiter service.

4. EK29 is a daytime service but pyjamas and amenity kits should be available.

You can order any item from the impressive menu at any time (although last orders for hot food are taken 90 minutes before landing, if memory serves). If you do not intend eating shortly after takeoff it might be a good idea to reserve the items you want in advance (on one occasion they had run out of what I wanted).

One thing to watch out for, possibly. When I left from the First lounge in concourse A the display at the gate went from showing nothing (not even flight number/destination ) straight to "final call" and there was no member of staff present allowing passengers through. When someone turned up, she said "It does that". I had a minor panic thinking the flight might go without me!

Apart from the A380s‘ showers, I prefer the 777. It has fewer First suites and the fuselage is larger. Perhaps the suites are larger, too.

Enjoy your first First experience!