Does the fact that Regina is still showing signs of redemption without her heart show that she truely is changing or is it poor writing?

Regina's different. Even without her heart in 3x03, she told Tink how much she genuinely loved Henry with a undeniable, loving look on her face.

Snow also said in this episode that she feels “deep” feelings with or without her heart. That Gina also feels things within her soul. I think that's beautiful! ;)

And the fact that Regina's heart is “resilient,” according to Belle, that it can someday be pure again! <3

I think the difference in behaviours between heartless Regina and Cora is due to a few reasons.

First is how long they'd been without a heart - Regina was missing her heart for a few weeks, maybe a month, while Cora had been heartless for decades (longer than Regina's entire life!). In general, characters who've lost their hearts for years, like Cora and Graham, display this emotional numbing effect, but characters who only have their hearts out for a shorter while have less of an effect.

The reason they took out their hearts might also play a role. Cora deliberately removed her heart to numb her own emotions. Regina took hers out to physically protect it. Maybe because Cora wanted the numbness, this amplified it.

Another possible reason could be the individual characters themselves. I always thought Cora was a bit metaphorically heartless anyway. She abandoned Zelena and left her to die long before she'd removed her heart. Maybe characters who are more emotional have less of this numbing effect.