Yes, they do stack.

Does hive barrier stack with Taken barrier?

Fallen, Hive, and Taken Barrier

It does not stack with itself. However, Taken Barrier will stack with Hive or Fallen barrier for 36% resistance to those enemies.

Can mods stack?

Mods will start yielding fewer benefits as you keep stacking the same ones on the same armour slot. In the example of the Hand Cannon Loader mod, using two of them will not double the reloading speed as one mod will provide only half the benefit, for a total of 150 per cent of the benefit a single mod would provide.