How to replace the copper connector under the bathroom faucet
Forget about epoxy for fixing that. The pipe is too damaged and being crushed in like that will definitely affect water pressure out of the faucet.
You're looking at cutting out the bad section and using compression fittings or sweating in a new section of pipe or just connecting the to ends after removing the damaged area.  Trying to do this under the sink would be a pain. I'd remove the faucet and do repairs, then reinstall the faucet.
You might even think about just replacing the faucet if the fixing part worries you.