There is no requirement at general law for you to have a business account, however you should check whether your bank’s terms and conditions for your personal account allow the account to be used for business purposes.
Any funds that you are holding on trust or in escrow should be held in a separate bank account that is named as a trust account or escrow account. This is so that the bank is made aware that the funds are not your personal or business funds and therefore cannot take possession of the funds to satisfy your personal or business debt.
As to whether you are providing a financial service, there isn’t enough information in your email above to determine this, you should look at the definition of financial services in section 5 of the Financial Service Providers (Registration and Dispute Resolution) Act 2008, http://www.legislation.govt.nz/act/public/2008/0097/latest/whole.html#DLM1109499. Depending on the nature of your service, it is possible that you might be operating a money or value transfer service (section 5(1)(f)). This is not my area of expertise, so if you have concerns on this should should contact a lawyer that has expertise in financial services.
You might want to look at having a company for personal liability reasons. It is quick, cheap and easy to incorporate a company online, and trading through a company means that (with some exceptions) you aren’t personally liable for the debts of the business. A company will however result in additional ongoing costs, e.g. preparing accounts and filing separate tax returns.
Hope this helps.