#1
It depends on the sound/feel you want. Recording all "Live" with vocals overdub gives a more, agressive/loose feel. But recording track by track, makes the whole sound alot tighter and mistake free. But, it really is down to you and the music you make. Most modern bands record each instrument seperatley, Although Iron Maiden & The Haunted record live. Hope this helped?
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#2
If you're planning to be a gigging band...either record it all together in a room or at least record all the parts all in one go. It will have a much more natural feel, and at least you know you can do it
And as for recording with a click track...only the drums should do that and only if they really have to. The best way, again, is to have the drummer know the approx. tempo the song is at then give a count in on the hi hat or something then just play. You don't want everything fitting absoultely perfectly together or it will sound robotic and with no feeling.
Record drums, then bass over drum track, then all guitar rhythm parts, then any seperate leads that arent played by the main guitar tracks, then any backing vocals if you need them, then main vocals. Then mix it down
#3
Like Metallica Metal, or Necrophagist Metal?

Metallica-esque Metal is probably better played at once, while Necrophagist/Technical Death Metal-esque would most likely sound best Played seperately then mixed in with the right volume's, tones, Ect.