On a basic single-stage system, often yes. On a heat pump, multi-stage, or variable-speed system, the wiring and programming are genuinely different, and getting them wrong causes short cycling, incorrect staging, or loss of heating or cooling. The frustrating part is that these look like equipment faults, so the real cause takes a while to find.

The common wire supplies continuous power to the thermostat, which a Wi-Fi model needs to stay connected rather than drawing from the system intermittently. Many older installations do not have one run to the thermostat location. Checking for it and aligning the wiring is part of the install, and it is the single most common obstacle to a smart thermostat working properly.

Almost certainly the reversing valve signal is wired or configured incorrectly. A heat pump makes heat by reversing its refrigerant cycle, and the thermostat tells it which way to run. Get that signal wrong and the system confidently does the opposite of what you asked. This is a configuration fix, not an equipment failure.

It can, mostly by removing unnecessary runtime rather than by cooling more efficiently. Scheduling around occupancy, work hours, overnight periods, and holidays is where the saving comes from, and across a Florida cooling season that runs most of the year, small reductions accumulate. A smart thermostat on a system with a duct or charge problem will not rescue it, though.

It can monitor humidity and manage cooling cycles with it in mind, and it can coordinate with a whole-home dehumidifier where one is installed. What it cannot do is remove moisture by itself. Where humidity stays high despite good temperature control, the answer is dedicated dehumidification with the thermostat configured to work alongside it.

A single thermostat measures one spot and treats it as the whole building. If rooms genuinely need different temperatures — a second storey, a west-facing room, a converted space — a smarter thermostat in one location will not fix that, and zoning will. If the rooms should already be even and are not, the problem is more likely ductwork than controls.