Yes, the gossip about Jay and Aliona is rife, but I don't think anything is going on, except he might have a bit of a crush on her.
As for Kristina, the first person she was accused of having an affair with was pro Vincent Simone and he has publicly admitted he didn't tell her he had just started seeing Susanna's his now wife. Kristina and Vincent only dated for a week on the Strictly tour before she broke it off when she found out about Susan. When Susan told him she was pregnant they were not a couple and it stayed that way for a while, with him saying he'd support the baby. Then later they formally became a couple. They're now married and have 2 children.
The second person Kristina is accused of having an affair with is Joe Calazaghe. He split from the mother of his children during the series and started a relationship with Kristina. He said the relationship between him and his girlfriend had been strained because he wouldn't marry her and meeting Kristina made him realise the relationship was over. Kristina was with Joe for 4 years and they split because he doesn't want any more children.
She met Ben Cohen on the show and I have no doubt his meeting Kristina had a lot to do with ending of his marriage, but when he left his wife he dated another woman for 3 months and Kristina was a friend. They are now a couple, but I don't lay the blame at her door for the break up of these relationships.
Kristina has been pilloried in the media and I hope her recent book sets the record straight.