SOFA status and gift tax

I am active duty on SOFA status, married to a Japanese national, employed by Japanese company.

We have signed for a house mortgage in which my spouse is the guarantor. My income will be used to pay for the mortgage.

I understand that there is a 1.1 million yen limit to the gift tax. My spouse is worried that she's breaking the tax law by just me giving her money to pay towards our house unless we pay all the necessary taxes. FYI, I plan to get my payment from the military for my housing allowance to pay the mortgage.

Is there any way around this?

If later we leave Japan (due to military orders) and want to rent it out to other military members, what should we do as far as taxes? From what we're thinking, the rent money would go from our property manager to my spouse's Japanese bank account. Would that then be categorized as income tax?