Good evening Sir.
Now that sounds like a great adventure worth investing in and I would say your little voice is taking good care of you.
I was there in 1999 and headed into Kanchenjunga which is in the top North Eastern corner of Nepal, close to the border with Tibet and Sikkim. It's an area less frequented by westerners and is more off the beaten track than places like Everest and the Annapurna circuit. We stopped with a remote village for a while (all planned) and helped them set the foundations for a new school. This might be something you could consider with your project - helping to improve education.
Without wanting to sound like a cliché, as alluded to by Tom, above, it changed my life. I was struck by how happy the children seemed, always with a smile, despite materialistically having nothing. This as opposed to western kids who by comparison have so much but never seem happy. I learnt that happiness comes from wanting what you have, not having what you want. For this reason your project really resonates with me. After I returned I had this notion burning a hole in my pants where I wanted to take a group of western kids for them to experience life from a different perspective by embedding them into a remote community. Make no bones about it, it would change their lives and, doubtless, yours too.
As you've said it's a 3rd world country. I vividly remember getting off of a Qatar airlines kite that was the height of luxury and straight onto the streets of Kathmandu where you're rubbing shoulders with poverty, lepers, and children who's limbs have been broken to enhance their begging ability. The people are generally as helpful and loyal as you can get. I've worked with Ghurkhas and once you've earned their respect they would fall on their sword for you.
As pointed out, water can be an issue including what appears to be the bottled stuff (recycled bottles are often refilled with contam'd water). I took a bottle of iodine and, if I can remember correctly, used one drop / litre. Iodine has the added bonus of being a useful antiseptic too - when travelling I like things that have a dual purpose.
I would highly recommend buying a copy of the Lonely Planet's Trekking in the Nepal Himalaya by Stan Armitage, and read it cover to cover. Whilst it is highly biased towards trekking routes it'll give you an idea of possible destinations and there's a huge amount on the culture, society, politics, top tips, health, etc.
I would also fully recommend hooking up with a tour guide before you go, whether it be for trekking, climbing or touring around Kathmandu or similar. They will help you safely maximise your experience. Simple things like meeting you at the airport, taking you to the hotel, tour guiding - stuff that can be difficult to arrange in the moment. I would also put some consideration to preparing the children fully before they go, so they are prepared for what they'll see.
As the Wiz said, depending on what your plans are altitude can be a potential problem, but one that can be easily mitigated if managed properly; given enough time and a sensible schedule most people can acclimatise easily enough. The problems start when folks start ignoring a few simple guidelines and / or ascend too quickly due to an unrealistic (and poorly planned) itinerary.
I really hope your project comes to fruition. Gosh, I'm getting all excited just talking about it and reliving my adventure. Drop me a PM if you want to discuss further old chap.
Good luck!
Returning from the mountains. L - R: 'Stampy' my old pal, Mahendra our guide, and me.