But I can't buy hjerim because the Stewart says there was some unpleasenants lately and nothing happens. And I haven't seen caliexto, do where is he around? I might pickpocket him to get the key and about lock picking I am the best at it as I got unbrakable perk so I have no problems with it.
You should definitely be able to buy Hjerim before starting Blood on the Ice or even during. You'll need the pamphlets from Hjerim to get the quest going, I think. After you have the pamphlets, talk to the old woman wandering around town and in the main inn. She's usually talking about the butcher.
This is a list of all of the ways to initiate the quest from wikia:
To initiate this quest, the Dragonborn must travel to Windhelm at around midnight. The Dark Brotherhood questline has been started or completed, it could hinder the possibilities of starting this quest.- In the graveyard, there will be several people gathered around a female corpse. The guard will approach the Dragonborn and start a conversation that leads to the initiation of the quest. To get to the graveyard, one should turn left at the entrance to the city, go through the archway, make the first right and go down the steps behind the Blacksmith.
- Buying the house http://elderscrolls.wikia.com/wiki/Hjerim in Windhelm will also start this quest.
- Another way to start the quest is to steal the key to Hjerim from http://elderscrolls.wikia.com/wiki/Tova_Shatter-Shield and enter the house. When one of the fliers located on a small dresser is taken, the quest will start at step 9.
- After questioning the three nearby witnesses, the Dragonborn should talk to the guard again.
- In order to be granted permission to help the investigation, the Dragonborn must visit http://elderscrolls.wikia.com/wiki/Jorleif, and then return to the guard.
- Inside the http://elderscrolls.wikia.com/wiki/Hall_of_the_Dead, the Dragonborn should speak with http://elderscrolls.wikia.com/wiki/Helgird.
- If the Key to Hjerim (purchased or pickpocketed) is in the possession of the player, the house can be entered to skip to step 9; otherwise, rfollowing the trail of blood in the crime scene will lead to http://elderscrolls.wikia.com/wiki/Hjerim.
- Advice should be sought by speaking to Jorleif.
- Entering the house can be done by picking the lock or receiving a key from the http://elderscrolls.wikia.com/wiki/Tova_Shatter-Shield, http://elderscrolls.wikia.com/wiki/Friga_Shatter-Shield's mother.
- All of the furniture that can be investigated should be.
- The http://elderscrolls.wikia.com/wiki/Butcher_Journal from the bloody chest up against the wall on the left of the entrance should be taken. The wardrobe on the right in the northwest room of the house will have a hidden door leading to an altar.
- From the altar, http://elderscrolls.wikia.com/wiki/Butcher_Journal#2 can be found.
- The http://elderscrolls.wikia.com/wiki/Strange_Amulet and pamphlets from the small dresser just next to the secret door should also be acquired. The amulet is hidden under the pamphlets.
- Jorleif will provide the player with information, suggesting to talk to http://elderscrolls.wikia.com/wiki/Calixto_Corrium and http://elderscrolls.wikia.com/wiki/Viola_Giordano.
- The Strange Amulet can be shown, and eventually sold, to http://elderscrolls.wikia.com/wiki/Calixto_Corrium. He will inform the Dragonborn that it belongs to the court mage. The amulet is needed in order to accuse the court wizard, although it is recommended to sell it or it will remain in the inventory indefinitely after the quest is completed.
- http://elderscrolls.wikia.com/wiki/Viola_Giordano is often found in http://elderscrolls.wikia.com/wiki/Candlehearth_Hall. She can't be talked to unless a copy of the "http://elderscrolls.wikia.com/wiki/Beware_the_Butcher" pamphlet is in possession, or if she's dead or missing. If the journal has been picked up the journal before talking to her in the house, it can be dropped and picked back up in front of her to continue the accusation quest line.
If none of that works, I would recommend just going around town and talking to every last person. If that doesn't work, it's probably not going to start and you'll need to start a new save to do it.
Also, I recommend reading the wikia page on this quest. There are a lot of bugs that can prevent it from starting/being completed correctly, so you should read through them to try and prevent it from happening again.
http://elderscrolls.wikia.com/wiki/Blood_on_the_Ice