I've been to all of your proposed countries besides Indonesia as a female alone. You should have no problem other than some harassment in Egypt. You'll just have to deal with it to see the great sights.
China - Keep in mind that you need your Chinese visa to extend to your time in Tibet so make sure you ask for enough time. Why not just get the Chinese visa in the USA before you leave? I think I had to enter within 180 days or something. You should be able to find that info on the Chinese embassy to the US website. I applied in person at the Chicago consulate, no problem. Otherwise, I suspect getting it in Bangkok might work out.
Cambodia - I got this visa at the Vietnamese border. Should be no problem getting it locally.
Vietnam - I got this in advance in the USA and it was much more expensive than getting it in China or Thailand. You'll pay more as a US citizen than Europeans.
Laos - I got this in Cambodia.
Nepal - I got this on the border with Tibet, $30. I don't remember if I needed a photo but bring some with you or get them made somewhere along the way.
Turkey - I was here a long time ago but I got the visa at the airport. It used to be $40 but I know they drastically reduced the price after I went.
Egypt - I got it at the border from Jordan (taking the ferry). $15. I had to pay in local curency but there was a bank to exchange right there.
Madagascar - I got it on arrival at the airport. $18 in US cash. If you want more than one month I think you need a letter and some bureaucracy... in French.
I don't really understand your route. If it were me I'd fly to Beijing and make my way to Tibet by train. Make sure you stop along the way to see other sites and cities. Make your way to Nepal by land and then fly from Kathmandu to Bangkok and tour SE Asia.
There aren't many flights to Madagascar (I was there this summer). From Europe you have to go through Air France. Actually, this is relatively cheap for the distance (like 600 euros) or there are many charter flights from France. From Africa you can fly through Nairobi (once a week on Air Madagascar) or J'Burg (a few flights a week). I flew from Nairobi for $612 round trip. I think you may also be able to fly through some of the islands East of Madagascar, possibly from Mumbai or Bangkok. Are you going to India to see it? If not then there may be other routes to Madagascar but none of them will be cheap. There are no flights from Cairo to Madagascar unless you go through Nairobi first. To go Cairo > Nairobi > Tana and back to Nairobi I bet you'd pay around $1,000. You could fly from Tana to France. Airfares from Europe to Egypt aren't too bad, a lot cheaper than flying from Cairo to the rest of Africa.
I would almost think about flying Bangkok> Cairo > Nairobi> Tana > Paris > Istanbul. Obviously, Madagascar will add considerable expense. It's not super cheap to travel in either. sure, it's cheaper than Europe but the high end European tourists that frequent the country drive prices up for anything tourist-related. And as most things are imported things like gas are expensive which makes the buses more than you'd think.
Okay, for RTW tickets I don't know. I have traveled twice with one-way tickets. I just bought a one way ticket to Asia and bought the rest along the way. I bought my ticket from Cairo to Ethiopia only like 3 days in advance! Search on travel web sites like travelocity, search on airline sites that serve your location. Call a RTW agent and see what they come up with. Keep in mind season may affect your price. Also be ware of the Olympic in China and October in China.
RTW tickets work great if you're flying to major cities. You might want to get a quote USA > China > (overland) > Bangkok > Cairo > Istanbul > USA. If you flew one-way to London first and bought a ticket there you might save some money. You would have to reverse your trip direction to do that. Be aware that some of the RTW tickets count any overland trips you take as miles toward your title. Check out which continent Egypt counts as (not usually included with Africa). Places like Madagascar may be harder to get to on a RTW ticket. It might be cheaper to do it as a side trip or see if Air France is on any of the plans you're looking at. But adding Africa to a RTW ticket usually adds a lot of cost.
I hope that makes sense, I was just spitting out the ideas to popped up when looking at your post. I have a list of all my airfares on this past RTW trip on my site. There should be a link in my signature below.
