What is the interpretation of "Many a disheveled, dust-covered person, if he were to swear by Allah, Allah would fulfill his oath," and does this mean that if I were to swear by Allah to fulfill something for me, He would do so? And is this permissible?

It is permissible for a righteous servant to swear by Allah in matters of beneficial righteousness. Allah's granting of the swearer's request is hoped for whoever is sincere and worthy of it. If the request is not granted in this world, Allah may postpone it until the Hereafter, or avert some evil with it. As for the aforementioned Hadith, it means that Allah looks at hearts, not outward appearances or wealth. The supplication of the disheveled and dusty person is more likely to be accepted than the supplication of someone who is outwardly adorned but inwardly corrupt. This means that Allah does not break His oath due to the oath-taker's honor with Him.