Does a new landlord have to honour informal arrangements the old landlord made with a tenant, like free parking?

Not automatically, but it is not always a clean no either. A truly casual, undocumented favour the previous landlord extended is generally not binding on a new owner simply because it existed before the sale. However, if an arrangement like included parking was genuinely part of what the tenant understood they were paying rent for, and can be shown to be a real term of the tenancy rather than a one-off favour, it may be treated as part of the tenancy itself, which does transfer with the property.

Because the line between a mere favour and an actual term of the tenancy depends on the specific facts, including how long the arrangement existed and how it was communicated, this is worth clarifying before closing rather than discovering a dispute afterward. Ask the seller directly, in writing, about any informal arrangements with the tenant, and have your lawyer assess whether anything described sounds like it could be considered part of the tenancy rather than a personal courtesy that ended when the previous owner sold the property.