I've taken the liberty of putting my comments and suggestions throughout your story, as well as some word changes I would like to see. I hope it helps.
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The land of the dead, was identical to the land of the living, apart from its obvious differences.
Humorous opening line. If you didn't intent it that way consider keeping it as a way to give your narrator a sense of humor. A jaded, dark humor if you prefer.
Earth was filled with clouds and blue skies. (Maybe you could tell us more about land-of-the-living type things like animals, rain forests and happiness) The importance of time and words affected the value and privileges such as friendship, work, family and identity.
However in death-land, time had paused, the souls (of what?) remained how they were when they died. The day and night was replaced by a dark grey atmosphere.
Reword this so it isn't in the passive voice: "A dark grey atmosphere replaced day and night."
The corpses (of who?), spirits, vampires and all the deceased spent their time here with eternal marks. All that remained from their lifetime was their memories, which gained the ability to reflect on their life. (How do memories reflect one their life?)
Along with many of these homeless souls was a man.
Try "Along with these many homeless souls was a man."
This man believed love was power and because of his extreme convictions, he sliced (sliced open?) his skin. He wanted to make sure that he had a powerful death. He had never regretted the suicide and felt after all the heartache throughout his life as a widowed man, it was worth every last drop of blood. That man was known as Crick.
Crick Gimsparnist (difficult name to swallow) followed his wife (what's her name?) into the noisy atmosphere of his local bar. His crisp blonde hair covered in bleach stood out to his dirty ragged clothes. His pale skin dangled around the dark bones on his skin. He was shaking his way to the bar. Crick smirked at the plump landlord, revealing his rotting teeth. “Evening Donald,” Crick croaked in a high pitched croaky (redundant) voice resembling a strangled frog.
“All right there, Crick?” Donald waved his hand as he patted Crick's bleached locks.
I have a pet peeve for the word "locks" when it's not talking about doors and keys. You don't need to keep reminding the reader about someone's hair, or at least not so soon after first describing it.
“What can I get you for this evening?”
“I shall have a pint of organ splash, please.”
“Coming right up, Crickie!” Donald's thumbs faced (thumbs should probably point rather than face) the ceiling as he pulled out the barrel.
“Can you believe it?” Crick dragged Anna's rags to his side, “I haven't had beer in three hundred years. I always liked mine chilled and freshly brewed. It was the taste of life.”
“I miss the good old days brewing the stuff. Here you go, that will be two coins.”
Since you didn't include a "said Donald" or similar line here I first assumed this line belonged to Anna because she was just mentioned and had to read it again.
“Thank you.” Crick passed two bronze coins over to Donald. He could always rely on Donald to reduce the prices, just for him. Every time he held his pint of organ splash, it reminded him of the beer he always loved before he died. The beer always cheered him up after his wife's death. Anna wasn't just a wife; she was Crick's life.
He never did recall how Anna died. (Ah, good, a mystery) He wanted to ask her for quite sometime. He just wished that Anna was more active in conversation. (Last three sentences started with 'He' - try rewording them) Crick fondled his spouse, (sounds dirty) his chin rested against her face. Anna Gimsparnist, his precious wife, was better known as Armless Anna, because her arms were sliced off before her death. Crick held his pint in his hands as he stood with a posture to show his pride. (Could you describe this posture? I have no image of what it might look like.) His cup was held high above his face and he tangled his spare fingers in Anna's long drained (dry? lifeless? limp?) curls, almost like Anna had died in water. “You seem to have had such a wet death I must say.”
“Crick,” Anna sighed, “do you even know how I died?”
“Well,” Crick replied, “I know you arms were sliced off before your afterlife.”
“For your information,” (This line feels too confrontational for someone who doesn't talk much.) Anna muttered to Crick, “my death bed was in the rocky bed of the canal!
Make it "My death bed was the rocky bed of the canal!" The "in" weakens it.
You can say your death was a peaceful one, but mine was painful. Sometimes, I wonder if you have any feelings for me.”
“Annie dearest.” Crick petted her shoulder, speaking in compassion. (Show us his compassion, ie., his cooing voice, etc.) “You know I ended my life to be reunited with you sweetie.”
“I see,” Anna sighed again (You don't need to describe her as sighing too often or you risk giving her a case of Sighing Woman Syndrome.) watching Crick as he drank. She despised his drinking habits with a passion. (a little cliche) One thing that Anna had learned in the afterlife was that her husband was never going to leave her alone. “I thought death would separate you from me.” (nice twist)
Crick almost spat his drink out. His hands collapsed onto the bar shaking his head. “Until Death do us part!” he roared with disgust. “I don't believe in that nonsense. Love lasts forever, even in death.” He moved (leaned?) closer to her ear, “That very day I married you, I was determined to make it last for all time.” Anna gulped as she felt his breath along with his words oozing into her brain. “We're stuck with each other and don't it feel good?”
Anna doesn't need to gulp here. It makes her seem unnecessarily wimpy and fearful, especially after her last line.
“Yes,” Anna gulped. Her body was trapped by aggressive fingers. (What, her whole body? Just her shoulder/head/hair/etc. would be enough to get the image of Crick holding her.) Crick brought his lips onto hers and pressed them against each other. (awkward wording, like he pressed his own lips together) “You sit down,” she requested (suggested? or even a simple 'said'?) pushing Crick off her as gently as possible. “I'll be right back.” Anna stormed off (she's angry now?) to the door trying to hide her embarrassment.
“Where are you going?” Crick asked leaping to his feet.
“Just going out for a walk,” Anna said without even facing him. “You go and have your pint.”
Anna nudged the door open with a weak shoulder. Her legs felt as light as a feather. She wiped her eyes with a feeling of defeat. Crick would never be able to understand her emotions. He made that clear from the tone of his voice. Even though she was dead, her soul was crying out for the freedom she never had. (good line) This was what a life was like without time and air. (maybe "time alone" or "space to breathe" would be in keeping with her frame of mind at the moment) The emptiness in her heart was overwhelming. She just wished that Crick could just back off. (Cut one or both "just" from here... too conversational) Why should their relationship matter anymore? Nothing about Crick seemed genuine to her at all.
Crick's total obsession with Anna created embarrassment. She didn't want to be known as Beer-Loving-Crick's wife. She wanted to be known as just Anna or even Armless-Anna was acceptable.
The wording here a bit jumbled. You could try making two sentences out of it. "She wanted to be known as just Anna. Even Armless-Anna was acceptable." or "She wanted to be known as just Anna or even Armless-Anna. That was acceptable."
Strolling down the dark alleyway reminded her of (removed a typo here) the darkness that was in her sleeping heart. (Try shortening to "the darkness in her sleeping heart") She wasn't going into a particular location, (You go to a location or in a direction, but not into) she just (another 'just' you can do without) had to go far away from her husband. Her steps became faster by the seconds until her strolling changed into running.
Loud sounds (what kind of sounds? a crash? a cry?) captured her attention. Seizing her feet, (??) she stood outside a wide door. The thick atmosphere could be felt from outside and it was the sort of thing Anna would love to see. She stepped into the building with no expectations of what would be inside.
I like where this is heading. I didn't care for Crick since he was pretty 2-dimensional and uninteresting. The second part looks pretty promising, too, continuing to develop the setting and plot with Anna striking out on her own.
I would read more, if there is more or if you plan to write more.