Is a vial of Poison consumed by the first attack of such a weapon or I get the +1d4 Poison damage for each attack I do in one minute?
Poison, Basic. You can use the poison in this vial to coat one slashing or piercing weapon or up to three pieces of Ammunition. Applying the poison takes an action. A creature hit by the Poisoned weapon or Ammunition must make a DC 10 Constitution saving throw or take 1d4 poison damage. Once applied, the poison retains potency for 1 minute before drying. (PHB, p. 153)
Rule as written I would say it would last for the full minute, unless there is another part i missed where it states otherwise?
Similarly, for Injury Poisons (DMG, p. 257), how long does the effect on the weapon last? (For example for Serpent Venom (Injury)).