:::"From what I understand, the Fed often uses the money it issues to buy assets, thereby getting richer through the creation & buying process according to basic logic..." 

 :::Wrong. Let's say that the Fed decides to buy government securities owned by Wells Fargo. The people at Wells Fargo and the people at the Fed decide that the securities in question are worth $10,000. What happens is that Wells Fargo transfers $10,000 of securities to the Fed, and the Fed transfers $10,000 of Federal Reserve notes to Wells Fargo (actually, more likely the Fed simply credits Wells Fargo's checking account at the Fed, but we're illustrating a point here). On the Fed's books, the Fed debits an asset account called "investment in government securities" (or whatever) for $10,000 and credits a liability account called "Federal Reserve notes outstanding" (or whatever) for $10,000. You have a balance entry, and there is no gain or loss on the transaction. If the value of the securities later goes UP to $11,000 and the Fed sells them for that amount, the Fed has a $1,000 gain  but that's no different than if YOU had bought the securities for $10,000 and sold them for $11,000. 

 :::Again, a Federal Reserve note is generally never "money" when its held by the Federal Reserve System. It's money for YOU when YOU hold the note. But as soon as that note is returned to the Federal Reserve System, its legal and economic substance is extinguished. The Fed cannot "owe money to itself." Similarly, you cannot "owe money to yourself" (at least not in the sense that we're talking about).