As a landlord, you can charge your tenant whatever rent the tenant is willing to pay.  Many leases are written to require the tenant to make separate payment for operating costs like taxes and utilities.  Others are just a single payment that is large enough to cover the landlord’s costs for such things.  The separate payments, to the extent that they can be separately identified, are a more accurate reflection of use and reduce the risk that you won’t get enough to cover the costs or that the tenant will pay for a whole lot more than it uses. 

When you ask about reducing your real estate taxes by renting to a “nonprofit,” I assume you are talking about a charitable nonprofit that might be entitled to a charitable exemption if it were the owner, not about one of the many other kinds of nonprofits that are not charitable.  (See Ready Reference Page: “What Do We Mean When We Say “Nonprofit”?).  This is a question of state law that varies by state.  Some permit an exemption only if the property is owned and utilized by a charitable organization.  Others allow an exemption if it is used by a charity even though owned by a for-profit owner. 

There may be other applicable taxes where the applicability differs by type of user.  Philadelphia, for example, has a City “use and occupancy” tax that applies to commercial tenants, but exempts charities.

You should ask a local real estate broker or real estate lawyer for advice on both of your questions.