I'm pretty particular about dumplings; whether gyoza (Japanese), mandu (Korean) or jiaozi (Chinese), I can spot a factory-made frozen batch from a mile away. That being said, HOMEMADE dumplings can be made and frozen, with no difference in taste once reheated.
I have yet to find a restaurant dumpling that can compare to the ones my mother makes; she kindly gave me her recipe to share with you. Making dumplings is a time-consuming and tedious process (hence why most restaurants use store-bought frozen ones), so I typically make a HUGE batch over the course of a lazy day and freeze them in bags to be cooked at my convenience. To cook them, you can steam them, boil them, deep-fry them, or do what I do - pan-fry them for a few minutes, then add water to the pan and steam them until done.
For the dumpling wrappers, make sure you purchase the ROUND wrappers, not to be confused with wonton/egg roll/spring roll wrappers. They are typically sold frozen in most Asian markets, and will need to be thawed about a day ahead of time. I also occasionally use a dumpling press when making gyoza, as I never mastered my mother's skill of perfectly folding and pleating each dumpling (I'm also incredibly impatient and easily frustrated).
For the sauce, you can buy a premade gyoza dipping sauce, or simply make your own. I usually make my own sauce, since I almost always already have the necessary ingredients.