Does a deathtouch creature with trample only assign 1 damage to each blocker?

Yes. With deathtouch, 1 damage is considered lethal for assignment purposes, so an attacker with both deathtouch and trample only needs to assign 1 to each blocker and can assign all remaining damage to the defending player.

Can a 1/1 with first strike and deathtouch kill a 10/10 and survive?

Yes, in a block. The 1/1 deals its deathtouch damage in the first-strike step, the 10/10 dies as a state-based action before the regular damage step, and so it never deals damage back to the 1/1. The first striker survives unharmed.

How does double strike with deathtouch affect a blocked attacker?

The double striker deals deathtouch damage in the first-strike step, killing the blocker before the regular step. In the regular step, with the blocker gone, a double strike creature with trample (or that's now unblocked) can deal its second hit, often through to the player.

First Strike, Double Strike & Deathtouch Interactions in Magic: The Gathering

Master how first strike, double strike, deathtouch, and trample combine in combat, including the famous deathtouch plus trample and first strike plus deathtouch cases.

How Combat Damage Steps Work

Normally all combat damage is dealt at the same time in a single combat damage step. First strike changes this: if any attacking or blocking creature has first strike or double strike, combat splits into two damage steps. In the first step, only creatures with first strike or double strike deal damage; in the second step, the remaining creatures (and any double strikers a second time) deal their damage. A creature that dies in the first step never deals damage in the second.

Double strike means a creature deals combat damage in both the first-strike step and the regular step. This is why a double strike creature effectively deals its power twice if both its targets survive the first hit. First strike alone deals damage once, but earlier, which can let it kill a blocker before that blocker deals damage back.

Deathtouch Plus First Strike

Deathtouch means any amount of damage greater than zero from that source is lethal. Combined with first strike, this is brutal: a 1/1 first striker with deathtouch can block or be blocked by a huge creature and kill it before it ever deals damage back, because the first-strike deathtouch damage is dealt in the first step and the creature dies as a state-based action before the regular step. The big creature simply never gets to swing.

Double strike plus deathtouch is similarly nasty. The creature assigns lethal damage in the first-strike step (one point is already lethal thanks to deathtouch), and the defending creature dies before the regular step. If the deathtouch creature is attacking an opponent rather than trading with a blocker, double strike still lets it deal damage twice to whatever it hits, but the deathtouch interaction matters most when a creature blocks or is blocked.

Deathtouch Plus Trample

Trample lets an attacker assign excess combat damage to the defending player after assigning lethal damage to blockers. Deathtouch changes what counts as 'lethal' for this purpose: with deathtouch, only 1 damage needs to be assigned to each blocker to be considered lethal, so the rest can trample over. A 5/5 with trample and deathtouch blocked by a 4/4 only needs to assign 1 to the blocker, letting 4 damage trample through to the player.

Combine all three (deathtouch, trample, and first or double strike) and the attacker can assign just 1 lethal point per blocker in the first-strike step, kill the blockers, and trample the rest through early. With double strike, it then deals its full power again in the regular step because the blockers are already dead, often hitting the defending player for a large second chunk of damage. These stacked keywords are why such creatures are so feared in combat.

FAQ

Does a deathtouch creature with trample only assign 1 damage to each blocker?: Yes. With deathtouch, 1 damage is considered lethal for assignment purposes, so an attacker with both deathtouch and trample only needs to assign 1 to each blocker and can assign all remaining damage to the defending player.
Can a 1/1 with first strike and deathtouch kill a 10/10 and survive?: Yes, in a block. The 1/1 deals its deathtouch damage in the first-strike step, the 10/10 dies as a state-based action before the regular damage step, and so it never deals damage back to the 1/1. The first striker survives unharmed.
How does double strike with deathtouch affect a blocked attacker?: The double striker deals deathtouch damage in the first-strike step, killing the blocker before the regular step. In the regular step, with the blocker gone, a double strike creature with trample (or that's now unblocked) can deal its second hit, often through to the player.