Soo... I am having a problem.

I noticed how the lockpicking skill does not increase when I unlock chests, only when I break lockpicks...

Another thing to mention here is that I am unable to increase my light armor skill through training. I have tried multiple times with Grelka in Riften, however when I pay for training it says that skill has increased but it does not count toward level up...

Anyone have this issue ?

I've found that chests I've already unlocked do not grant skill exp if I go back to them after a cell has respawned.

As for the armor thing, try leveling your armor skill a bit in combat and then buying training. Sometimes if the skill is on the cusp of leveling up, it bugs and won't yield character level exp from training.

Edited for clarity.

Okay, thank you for the suggestion.