1
Check your PM's as I just responded to your message.It is relatively easy to get from Eilat to Cairo. The "best" way (I realize that's subjective, but when one considers price, comfort and time, I think it's the best) is to take a shared taxi directly from the border to Cairo. Of course, there has to be someone there you can share the taxi with.
If you take the bus you need to walk about 1k from the border to the bus stop, then wait for the bus (there is one at 4:30pm, but there may be an earlier one as well).
As long as you use common sense and stay clear of any demonstrations it's plenty safe.
4
Yes, the border is easy (assuming you have nothing in your background which would cause alarm).Keep in mind, you'll need an all Egypt visa prior to arriving at the border crossing. They are not issued at the border. They are issued at the consulate in Eilat or the embassy in Tel Aviv and take about a day to get. You'll have plenty of time to get one, but you must get one.
There is an Israeli exit tax of around 100NIS and an Egyptian entry tax. You'll get nicked twice by the Egypt; once at the border and again just outside Taba on the way to Cairo. I don't remember how much, but it isn't much.
Good luck.

