for (1), i believe airlines are quite understanding towards mummies with young babies so you should be able to make the special request before flight. call the hotline to enquire to confirm if you wish. i dont't have personal experience to share though, because my boy still latches on directly whenever i am with him and i latch him at take-off and landing to avoid discomfort in his ears caused by the change in air pressure.
for (2), yes, i bring my pump along with me. when my boy was younger, it was just in case he slept thru the nite and i needed to empty my breasts so that my supply would not be affected. now that he is older, it is more for pumping out some milk to add to his breakfast cereals.
as for (4), have you already started your 4-month-old on semi-solids? if so, what are you feeding her? i only introduced semi-solids to my boy after he turned 6 months old, and for the first month, we stuck with organic breakfast cereals only for one meal. it was breastmilk at all other times. so it was very easy and light travelling with him in tow. =)
my advice would be that if you have not introduced semi-solid to your baby, dont't suddenly do so during the travel or just a few days before because you want to give enough time for your gal to get used to it, and also watch out for any possible allergy. at her young age, milk is good enough to fill her up. even if you have already started introducing semi-solids, it is ok to go back to full milk for those few days of your tour. she won't notice the difference. there is no need to complicate your travelling.
sorry can't advise on (3) cos the last time i was there, i wasn't pregnant and so wasn't looking out for nursery rooms! =)