777 is not exactly my cup of tea, so i would try answering the other two questions.
1. We have 3 ways to change our altitude in a boeing...LVL CHG, V/S and VNAV.
VNAV follows the programmed path in the FMC and will follow all the speed restrictions and, where present, the altitude restrictions. That is, it will automatically slow the airplane at 10000 ft to 250 KIAS and so on
V/S will follow the rate of descent or climb as set in the MCP and will follow the rate, even if it means your speed inc or dec as a result. In V/S, the pilot will keep an eye or rather he
better keep an eye on the speed.
LVL CHG is the basic mode so to speak. No complicated requirements.....just max thrust if you want to climb, and idle thrust if you want to descent.....and it flies a pitch attitude which will maintain the selected speed.
Now as far their using is concerned, VNAV is used in almost all stages of flight, as it , once programmed, will automatically do what you tell it to do. V/S is normally used for altitude changes of 1000ft or less. And LVL CHG for altitude changes of more than 1000 ft.
2. Main difference between flg with AP engaged and AP disengaged.....in one case, you have to fly the plane and monitor the flt progress while in the other you only monitor .
PS: Sorry for the extra long post.....my post here you see...i guess i got a bit carried away
...anyways hope this helps