It takes 1 second to charge, and her maneuverability is limited - she can dodge obstacles but has to stop briefly to make sharp turns. However, she can also use it to fly. There is no time limit.
He came back partially about a minute or two after being erased so that he could give Negi advice, then disintegrated again.
A fight sequence with Jack and Eva
Endless White Nine Heavens should be able to trap Doomsday.Spoiler
http://www.mangareader.net/mahou-sensei-negima/331/2
http://www.mangareader.net/mahou-sensei-negima/331/3
http://www.mangareader.net/mahou-sensei-negima/331/12
http://www.mangareader.net/mahou-sensei-negima/332/2
http://www.mangareader.net/mahou-sensei-negima/332/3
http://www.mangareader.net/mahou-sensei-negima/332/4
http://www.mangareader.net/mahou-sensei-negima/332/7
http://www.mangareader.net/mahou-sensei-negima/332/9
http://www.mangareader.net/mahou-sensei-negima/333/5
http://www.mangareader.net/mahou-sensei-negima/333/6
http://www.mangareader.net/mahou-sensei-negima/333/7
http://www.mangareader.net/mahou-sensei-negima/333/8
http://www.mangareader.net/mahou-sensei-negima/333/9
http://www.mangareader.net/mahou-sensei-negima/333/10
http://www.mangareader.net/mahou-sensei-negima/333/11
http://www.mangareader.net/mahou-sensei-negima/333/12
Another fight with Eva in these two chapters.