How good are you at forgiving those who have wronged you?
This pivots entirely on the expression of remorse and display of effort from the other. If anything, I'm too capable. There are scenarios though where I slam the gavel and issue a life sentence with no chance for appeal, but it's extremely rare.
Do you feel that the ability to forgive is a valuable and necessary trait?
Obviously. To lack this ability is to expect perfection, which does not exist.
Have you ever desired forgiveness and was denied it?
Hmmm, I'm not sure but I want to say no. I've asked for forgiveness simultaneously hoping to not be rejected, and still been rejected, but I don't think that's the same as not being forgiven.
In my experience, nothing is more painful than forgiving someone who perhaps doesn't deserve it, and then somehow still being rejected/abandoned by them anyway. It's been a lesson to me to be more discerning in whom I choose to forgive.
If so, how did that make you feel?
Well, like I said, I'm usually forgiven when I express remorse and effort. The latter situation mentioned above feels like shit.
Pro Tip: Don't hold onto people who make you feel like shit, or hurt you, ask for forgiveness, and then again hurt/abandon you anyway.
Edit: I thought of one time I asked for forgiveness and wasn't granted it. It felt awful, for a really long time. I don't find communication uncomfortable enough to avoid, especially when it can solve a problem and save a relationship, so I find that reaction in others perplexing.