The rent barely covers the costs. Can I reduce the insurance?
Some of it sensibly, some of it never. Raising the deductible is a legitimate lever if the figure is one you could pay. Cutting liability is not, because that exposure is not bounded by what the house is worth and it is the cheapest part of the policy.
Do I really need loss of rent on a small property?
Arguably more than a large owner does. If a fire stops the rent for months, your mortgage and taxes continue and you have no other rental to absorb it. It costs little and it is what prevents one loss from ending the investment.
What is the minimum I should carry?
A dwelling limit that could actually rebuild it, a liability limit well above the default, loss of rent matched to the real rent, and a deductible you could write a check for. That is the honest floor, and we will quote it alongside whatever you are paying now.