will the IQ4 work with all my sensors and thermostat?
The 345Mhz version that I linked will work with your 2GIG/Honeywell 345Mhz sensors yes.
It will not work with E-series 2GIG sensors, but if your panel is 7 years old it is not an encrypted E-series model so that is not relevant.
Z-wave thermostat support would depend on the model. What model of thermostat are you using?
the upgrade LTE is the verizon one?
The 2GIG GC2 switch kit includes the Verizon model of cell module, yes.