I have no information about the present ownership of the house or how this financial "gift" is handled. If you want to know how your transactions would affect your benefits, you have to tell us about the transactions.
As a general rule of thumb, when there's a possibility of being accused of an offense such as welfare fraud, it makes sense to err on the side of caution. If you don't want to explain the situation here, see if you can get some help from legal aid.

