Adric, Mathematical Genius

If the ability has damage divided as it was put onto the stack, the division can't be changed, although the targets receiving that damage still can. The same is true of abilities that distribute counters.

Adric, Mathematical Genius's first ability targets an activated or triggered ability that is on the stack and creates another instance of that ability on the stack. It doesn't cause any object to gain an ability.

The Doctor's companion ability allows you to have two commanders if one has the ability and the other is a legendary creature that is a Time Lord Doctor and has no other creature types. Creatures with the changeling ability, for example, can't be a second commander this way.