Regarding mortgaging, there's no obvious advantage to having two mortgages - even if lenders will allow it, which they are unlikely to do. You should get a joint mortgage for the ful amount required, and make any necessary agreements between yourselves on how you service the mortgage. The simplest thing is probably to set up a joint account into which rental income and any top-up financing goes, and have the mortgage direct debited from there. Account fees will be tax deductible as a business expense.
And I second ClubMan's recommendation that you put a legal agreement in place - as a bare minimum, something both of you countersign and retain copies of, even if you're not going to have it officially witnessed by your solicitor. Property rows in families are incredibly damaging to the families caught up in them, so you're best setting out all of the expectations and agreements in advance. That way, if things go pear shaped, you know how to deal with it, and you've a much better chance of keeping good relationships.