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aq and g are state symbols. If a reaction has multiple sate symbols, it is heterogeneous, so yes, it can occur. If the state symbols are the same, it is a homogeneous reaction. Kp and Kc are just measures of concentration or pressure, so it depends what you are looking for in the reaction.
Yes, there could be an instance in which a reaction includes reactants or products that are in (aq) and (g) states. If so, you would need to convert partial pressure to concentration through PV = nRT. This equation can be manipulated to n/V = P/RT, in which n/V is molar concentration.
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