Could it be that he killed and ate the girl who imprisoned Veldora? Because I see that his/her appearance is so similar to her...
Your observation that his human form looks similar to Shizue is spot on. I'm not sure exactly how far the anime has progressed, but based on Wikipedia, they should have just left after meeting the Dwarf King, Gazel Dwargo.
In the coming episodes, we will be introduced to Shizue's character and her backstory.
As far as I know she doesn't really have any relation to the imprisonment of Veldora (the wiki doesn't mention anything either). Possible reason for confusion explained at the end.
Yes, he absorbs Shizue, and is indirectly the cause for her death. However, it was Shizue's request that he absorb her, and his actions were to save her. So there was no enmity.
Shizue is also a Japanese, but unlike Rimuru who was reincarnated, she was summoned to this world by the Demon Lord Leon Cromwell. He then proceeds to make her the host for Ifrit, a high ranking flame spirit, in order to let her survive the summoning ordeal. He then proceeds to use her as a tool, a general in his armies. She is later saved by the Hero when Leon Cromwell escapes, and she uses the Anti-Demon Mask to keep Ifrit suppressed.
Meeting with Rimuru:
Shizue meets Rimuru when she joins a party of adventurers heading to the forest to investigate Veldora's disappearance. This is the same party we see earlier, when Rimuru first escapes the cave as a slime. Rimuru saves them while they are being chased by monsters, and they grow to trust him though he's a monster.
How Rimuru gets the human form:
Rimuru and Shizue bond a lot over their common nationality, and he shows her visions of how the country has changed since her time. When Shizue whose life force is weakening gets taken over by Ifrit, Rimuru defeats and absorbs Ifrit using the Predator skill, leaving Shizue unharmed. However, with the source of her powers gone, Shizue cannot survive much longer and rapidly ages. She passes on her will to Rimuru, which is to defeat Demon Lord Cromwell who caused her such hardships, and to take care of her regrets - 5 children she was teaching, and 2 individuals. She requests Rimuru to put her to rest within himself, and he absorbs her and takes on a form that is quite similar to her in appearance.
I hope that answers all your questions.
Veldora indeed mentions that he was trapped by the Yuusha or Hero, who was a pretty girl with snow-white skin and silver black hair in a ponytail. However, this is not Shizue. Shizue is saved by this same hero, as mentioned earlier. I am following the Manga, and no further details have been given about the Hero, but you should be able to find a lot of information on the Wiki.