Wouldn't reducing Fed Balance Sheet lead to Inverted Yield Curve? BACKGROUND

I am involved in finance, but by no means an economist. I've been reading Ben Bernanke's "The Courage to Act" and have become interested in QE1 and QE2. Currently, I am trying to understand the Fed's Balance sheet reduction.

NOTE: Apologies if some of my assumptions/questions are misguided

ASSUMPTIONS


QE was a fiscal strategy to lower long-term interest rates
Fed bought Treasury securities and Mortgage-backed Securities to reduce long-term interest rates
Fed is currently looking to reduce Balance sheet to raise long-term interest rates to pre-recession levels (including short-term interest rates)  
The Fed is looking to raise short-term interest rates first, then long-term interest rates


QUESTION(S)


If the Fed raises short-term interest rates, but keeps long-term interest rates low, wouldn't this create an Inverted Yield Curve?
Aren't Inverted Yield Curves an indicator of recession?  
Why isn't it better to raise on long-term interest rates first, and then raise short-term interest rates?
As a preface to my answers, I want to point out that bond yields are set in the market. We can think of bond yields as being (roughly) the sum of the expected path of short rates over the life of the bond, plus a term premium.

QE may or may not have lowered term premia (which would lower yields), but that is not enough for the Fed to completely set interest rates independent of what bond market participants expect the path of short rates to be.


The Fed may want to keep bond yields low when raising rates, but bond market participants will not want to own bonds that they expect to lose money on. Therefore, it would be extremely difficult for the Fed to keep bond yields down if they are in the process of raising short rates. As a result, it is difficult for the curve (overnight - bond maturity) to invert when rate hikes are expected.
Yes, inverted yield curves have been historically associated with recessions in the United States. This is an indication that the bond market is pricing future rate cuts. (The curve will have difficulties inverting if short rates are zero, as has been the case in Japan.)
The raising of bond yields is done by people who expect rate hikes, not by a Fed decision. Since the private sector does not exclusively borrow on a short-term basis (for example mortgages), this presumably has an effect on the economy. As a result, it is part of the "transmission mechanism" from the policy rate to the economy, and so it is not really better or worse than raising the short-term rate.