I was wondering if it's generally a good idea to pair beer-based recipes with the same beer that you use to cook them. For instance, should you drink a Guinness with Beef and Guinness Stew? Should you drink the same beer that you use to make your batter when you make Beer Battered Fish and Chips?
There is no culinary basis to make that generalization. The choice of beer (or wine or any other ingredient used to add depth) may be selected to enhance, balance, contrast, or even counteract one of the other ingredients. But that doesn't necessarily make it the beverage of choice to accompany the resulting dish.
The beer-as-an-ingredient may not even be the dominant flavor of the dish. And if it is the dominant flavor, that doesn't necessarily mean "more of the same" is the best accompaniment.
For example, (I'm drawing an analogy) I might add a dry white wine to a pasta sauce to add depth or a sweeter white wine to help cut acidity. But tomato-based pasta dishes are traditionally accompanied by a red wine, not white.
These are broad generalizations, but there's nothing to say that my favorite bread recipe enhanced with a light lager must (or even preferably) be matched with a lager.
It's the overall flavor of the dish that determines the best accompaniment. Not the beer ingredient.
Definitely yes. you could add the beer of your choice to add some extra flavour to the sauce and enjoy the whole dish with a nice beer at the right temperature.
For the right temperature I would refere to that: What temperature should I serve my beer?
In my humble opinion, you can also refine your stew with wine and drink the same one while eating.