Is it permissible for a Muslim who is not a student of knowledge, but who strives to research Islamic rulings by reviewing the sayings of scholars, drawing conclusions from what is strong, following reliable fatwas, and adopting the easier opinion in extenuating circumstances, to continue upon this method, or must he adhere to a specific madhhab?

You are not at fault for what you mentioned. A common person is not obligated to adhere to a specific madhhab (school of thought). Their duty, if they are not among the people of knowledge, is to ask scholars and act according to what they are instructed. They are also permitted to ask others. If they possess the tools of knowledge, then they should act according to what they find most likely to be correct. Taking a concession sometimes out of necessity is permissible, as Al-Subki said: "It is permissible for the ignorant to follow [a scholar] and to take a concession from the sayings of scholars at times when there is a pressing need, without constantly seeking out concessions. From this perspective, it is valid to say that disagreement is a mercy, for concessions are a mercy."