Tanks who play on controller.

[ItMe]

I want to find out, is there any reason to use Cover?
It is really tricky to target someone with it, so they usually get hit/die before I can actually do something.

I've learned the hard way that if you are not talking with your healers in voice chat... don't use cover*.
If the other character would have taken enough damage they die, by using cover suddenly you'll be taking a bunch of extra damage out of nowhere and even if you macro to say you're using cover on [target], this catches healers by surprise often enough that you'll die more than you're comfortable with. And usually a tank going down is a much bigger issue than a DPS going down.

*using cover to save clerics though is a total Chad move and you should totally do it.

Also I used my chocobo new player silver feathers on the sword and shield of Magitek, was this the wrong thing to do?

There is no wrong way to use silver feathers.
There are no unique items they buy, so there is nothing you could be missing out on.