Indestructible creatures also ignore deathtouch. Normally, a creature is destroyed if it takes damage from a creature with deathtouch. But since indestructible creatures can't be destroyed, they're immune.

Does indestructible override Deathtouch?

For question 2, indestructible creatures are immune to deathtouch because they are not affected by destroy affects. Deathtouch also isn't much help against creatures that can regenerate.

Can a creature with indestructible die from Deathtouch?

Even when they battle creatures with deathtouch, creatures with indestructible come out on top. However, indestructible does have its limitations. If a creature's toughness is reduced to zero, it still dies, even if it has indestructible.