Can I divide up mortgage interest paid (1098 received in both names) between two unmarried people who co-own and co-habitate? What if one partner can make more use of the write off than the other due to other itemized deductions on schedule A when the other partner will still get the standard deduction even if they take half of the mortgage interest?

Can I divide up mortgage interest paid (1098 received in both names) between two unmarried people who co-own and co-habitate?”----->Yes, you can; interest on ANY loan can be deducted only if the person claiming the deduction is LEGALLY LIABLE to pay the loan.Now, if you and your co-habitant are jointly and severally liable for the mortgage, then you can split the interest any way you see fit.
“What if one partner can make more use of the write off than the other due to other itemized deductions on schedule A when the other partner will still get the standard deduction even if they take half of the mortgage interest?”---->The partner can’t claim both standard deduction and itemized deductions at the same time. If he wants to get the standard deduction, then he can’t claim itemized deductions, mortgage interest expenses deduction, on Sch A. On the contrary, if he doesn’t want to claim itemized deductions, then he can get standard deduction on his return.
Just for reference; if you are married and file separately and your spouse itemized deductions, then you must also itemize deductions, even though this is less than the standard deduction to which you would otherwise be entitled.