Egyptian escapade

Welcome, Basically most of the answers to your questions are yes.

Two weeks will allow you to see most of the interesting sites along the Nile. It's easy to get from place to place. You don't have to pre-plan and it's pretty safe. You can find guides as you go. You will get hassled because everyone gets hassled. Use common sense precautions, avoid areas where there are demonstrations and stay current on events, especially in the area you're in.

You will save money seeing the country on your own. The only no is that it is not an expensive country.

Good luck.

It's safe and you're likely to have much more fun this way. My only advice is: buy a LP guide so you can have a list of proper hotels at all prices. Also note that there has been a number of people reporting handbag snatching, so better carry a backpack or a money belt. As for harassment people will try to sell you stuff any time you put a foot in touristic sites, but it's not that bad and telling people you live in Cairo and are an expat sometimes helps. I strongly suggest you also visit less touristy sites such as the wonderful Islamic Cairo neighbourhood, where there is no such hassle.

Yes for sure it's doable and it will also be a blast. The people there will treat you very well. There are some agressive touts but its no different then in other countries and they are usually just in tourist markets and tourist sites. In 2 weeks you could see the Pyramids, and the Nile and maybe even make it East to do some snorkelling/diving in the stunning Red Sea.
If your worried about your safety you should read this article: Is Egypt Safe To Travel?
For everything you need to know about travelling in Egypt including weather, costs, accommodation, sites and off the beaten path secrets see this Budget Guide To Egypt For tips on Luxor check out our Luxor Blog
If you sail the Nile, which is VERY RECOMMENDED then get some tips here: Nile River Felucca Journey
Hope this helps! Enjoy Egypt. It's an amazing place!
Goats On The Road

It is certainly doable and you will have a deeper experience of the country and the people than on a group tour. We are two women (40s) and have been travelling in Egypt several times on our own (http://westwards.typepad.com/westwards/egypt). You will likely get unwanted attention, not only from people who want to sell something or get you onto their caleche, but occasionally there may also be men making indecent gestures or offers. In such a case, do not hesitate to be very angry and shout (English is fine; these men know it's not ok what they are doing). Usually they go away or other people will help. But this really does not happen regularly.
Egypt is not a dangerous country like let's say Guatemala. You should be fine if you are careful, and most people are really nice and have a good sense of humour. You might also be lucky and find a good guide on your own, but don't rely on finding good guides on the spot. Better bring your own guidebooks and explore for yourself. Or try to eardrop on the groups, they usually have ok guides. And be prepared to bargain and haggle. Do not see it as a rip-off, but as a sport you can get better in.
Right now Egypt is quite cheap, not many tourists and a lot of competition. So if you go on your own you also will help the local people, because your money does not go to the big travel companies. And the local people really do need the income from the tourists.