Yes, but only if the deathtouch is given before damage calculation (the assignment of damage). If it’s after the fact, then you’ll still kill all of the creatures through deathtouch, but you’ll not be able to assign 1 damage to each of them to best use the trample.

702.18b The controller of an attacking creature with trample first assigns damage to the creature(s) blocking it. Once all those blocking creatures are assigned lethal damage, any remaining damage is assigned as its controller chooses among those blocking creatures and the player or planeswalker the creature is attacking. When checking for assigned lethal damage, take into account damage already marked on the creature and damage from other creatures that’s being assigned during the same combat damage step, but not any abilities or effects that might change the amount of damage that’s actually dealt. The attacking creature’s controller need not assign lethal damage to all those blocking creatures but in that case can’t assign any damage to the player or planeswalker it’s attacking.

702.2b Any nonzero amount of combat damage assigned to a creature by a source with deathtouch is considered to be lethal damage, regardless of that creature’s toughness. See rules 510.1c–d.

Since the creature has been under your control since before your turn, you can attack/activate tap abilities on your turn.

302.6. A creature’s activated ability with the tap symbol or the untap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since his or her most recent turn began. A creature can’t attack unless it has been under its controller’s control continuously since his or her most recent turn began. This rule is informally called the “summoning sickness” rule.

<3 Cheers!