Really it all depends on the type of agreement you enter into with the owner of the property. If you do a mortgage, then you, as the buyer would be responsible for paying taxes and homeowner's insurance. However, some lease/purchase arrangements are done through rental leases, with some portion of the payment going toward the purchase. If this is the type of arrangement that you enter into, then the owner of the property would likely still pay the taxes and insurance, because ownership would still rest with him/her. You should always seek competent legal advice if you are entering into an agreement and have doubts or questions about what is happening.

GREAT QUESTION: It all depends on how the contract is authored. Many property owners prefer these amounts are configured in your monthly payment where they pay. Insurance would be paid by property owener for exterior only you most likely need to get your own insurance for personal content.
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In my experiences, you can write the contract either way. Most often the monthly payment that is determined to be paid by the person leasing the property will have the taxes and insurance figured in. But you need to remember that you are still the owner of the property, tax bills and home owners insurance is still in your name. It is your responsibility to be sure they are paid. Until the transaction is final, you are still, per say, the owner of the property under contract. You can also require them to carry renters insurance for their own personal properties, which I definitely recommend. Hope this helps.