All of these are internal questions. Allowing you to temporarily reduce your working days by taking unpaid leave one day a week isn't parental leave in an official sense. Parental leave has to be taken in blocks of a week, unless it is for a disabled child, and comes with certain rights.
Your work are allowing you something different, so therefore the terms and conditions of that arrangement are up to them. As it's a temporary arrangement and is using unpaid leave rather than a reduction in contractual hours, my guess would be that your holiday entitlement would be unaffected - apart from anything it would be an administrative headache to do anything else. But as this type of 'parental leave' isn't a legal thing, I can't say that for definite.
I assume you've checked your work's policy and it doesn't address this issue, in which case you'll need to ask HR how it works.
With regards to occupational maternity pay, again this isn't a legal thing and your employer can set whatever terms and conditions it likes. We don't know what those are. If their policy contains no definition of what "full pay" means, you'll need to check. Normally you'd expect it to contain more detail, particularly as women often reduce their hours temporarily at the end of maternity leave. Does "full pay" mean the permanent salary on their contract? Does it mean "full pay" at the time they actually go on maternity leave, or at the qualifying week, or another date? Where someone's pay varies, is it averaged and if so, how is that calculated? Where someone takes unpaid leave as you are doing, what figure is used. These are all questions for your employer's policy, and if not in the policy, for HR.