If your ex has bought a house and is cohabiting it is relevant, yes, because it affects her needs. In most ordinary cases needs are very important in determining the outcome. You will also be entitled to know the financial circumstances of her cohabitee. That's not because you can claim anything from him but his financial circumstances are also relevant to your ex's needs.
As to the costs of a pension sharing order, no, they very likely cannot be avoided if a pension sharing order is an appropriate part of the outcome.