We were at the science museum today and the queue for the natural history museum was at both doors -neither too bad though. I would check both doors. Incidentally there was no queue for the science museum or the V&A so you do have alternatives right there if the queue is prohibitive, though I'm sure it is the NHM you want.
Agree with the others to take your own food.
I've never been on the eye but I would guess first thing would be best in terms of queuing, and if you are right next door that might work? Apart from that it will be weather dependant in terms of getting better views. My preference would be day time rather than dark evening (not that they are so dark now) as lights are pretty but it's nicer to see what you are looking at!
South Ken will be ok with a buggy if you have someone else with you to lift.
Not sure about trains but think RtR is probably right. And yes, st pancras definitely easiest for eating before your journey. I really like that station too.
ETA have a great trip! And I don't know whether you ended up organising a meet but when I replied to your original post about that I forgot I would be back at work

was looking forward to meeting you! Maybe I'll have to come to Yorkshire instead one day
