The ability itself on Teferi's Veil triggers when the creature attacks. The creature has to attack before Veil does anything, so, if it does, that will trigger abilities that also trigger from that creature attacking.
End of Combat is the step at the end of the combat phase. It's after the Combat Damage step, so it is after creatures in combat have dealt combat damage. Teferi's Veil 's ability doesn't do anything even right after its ability resolves, but it creates a delayed triggered ability that triggers "at end of combat". This is the ability which phases the creature out.
edit: Also, the creatures the Veil affects are not enchanted by it, since that word means an Aura is attached to the creature.
If teferi's veil is put into play by a triggered ability "when attacks put it into the battlefield" does that creature phase out after the combat phase?
Or does the effect of teferi's veil only trigger when a creature attacks (which may be different from when a creature is attacking)?
If teferi's veil is put into play by a triggered ability "when attacks put it into the battlefield" does that creature phase out after the combat phase?
Or does the effect of teferi's veil only trigger when a creature attacks (which may be different from when a creature is attacking)?
Teferi's Veil only checks for creatures that are declared as attackers. At no other point will it look at who is attacking and phase out those creatures. So if it isn't on the battlefield when attackers are declared it didn't "see" any attackers being declared.
Does activating the ability of vanishing prevents removal of the enchanted creatures and whatever is attached to it from boardwipes?
In general, a permanent that's phased out is treated as nonexistent and unaffected by the game, "[e]xcept for rules and effects that specifically mention phased-out permanents" (C.R. 702.26b). For example, none of the six spells named below will affect a phased-out permanent. Moreover, when "a permanent phases out, any Auras, Equipment, or Fortifications attached to that permanent phase out at the same time" (C.R. 702.26g).
Note that the game has no notion of "board wipes" as such. There are numerous spells that can negatively affect all permanents of a certain kind on the battlefield at the same time — Wrath of God, Blasphemous Act, Armageddon, Obliterate, Upheaval, Decree of Annihilation, and so on — and they don't all affect the permanents they apply to in the same way.
If the creature has an ability that triggers when attacking does it still trigger if enchanted by teferi's veil?
End of Combat is the step at the end of the combat phase. It's after the Combat Damage step, so it is after creatures in combat have dealt combat damage. Teferi's Veil 's ability doesn't do anything even right after its ability resolves, but it creates a delayed triggered ability that triggers "at end of combat". This is the ability which phases the creature out.
edit: Also, the creatures the Veil affects are not enchanted by it, since that word means an Aura is attached to the creature.
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Can fierce guardianship be cast without paying its mana cost while your commander is phased out?
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Or does the effect of teferi's veil only trigger when a creature attacks (which may be different from when a creature is attacking)?
Note that the game has no notion of "board wipes" as such. There are numerous spells that can negatively affect all permanents of a certain kind on the battlefield at the same time — Wrath of God, Blasphemous Act, Armageddon, Obliterate, Upheaval, Decree of Annihilation, and so on — and they don't all affect the permanents they apply to in the same way.