First questions easy, yes.
You can offer more than the statutory amounts if you have a company maternity scheme. You must make sure your maternity leave and pay policies are clear and available to staff.
www.gov.uk/employers-maternity-pay-leave/entitlement
Second question is more interesting and a logical guess rather than a legal answer, but I saw the google challenge and couldn't resist 
So you want to pay maternity leave, and pay them for working? That doesn't make any sense, you wouldn't pay them twice.
can the employer choose to continue to pay them in full during maternity leave?
As the employer, you can pay them as much as you want, as long as you meet the statuary minimum maternity requirements, ie you let them have maternity leave without having to work.
If the employee gives up their rights to maternity leave to return to work, either home or office, then that's up to them.
Does that help?