Does Jesus provide emotional healing? Or not? If so, how?
Yes Jesus heals the entire person, spirit, soul and body, it's part of the gospel:
Luke 4:18
18 “ The Spirit of the LORD is upon Me,
Because He has anointed Me
To preach the gospel to the poor;
He has sent Me to heal the brokenhearted,
To proclaim liberty to the captives
And recovery of sight to the blind,
To set at liberty those who are oppressed;
19 To proclaim the acceptable year of the LORD.”
There are many ways that Jesus heals, as there are many ways a person gets wounded.
Some times it's just asking him, praying and fasting, spending time with Him in His presence, there are times of forgiveness if there was an offense by another person before some healing can set in (also physically), there are instances deeper deliverance is needed if there is a stronghold in a person created by a wounded soul... it all depends on the situation.
In any case, it's His specialty and He is really good at it...