Hi
AC goes into a rectifier to produce DC
DC goes into an inverter to produce AC
Your pronunciation seems right.
You do have loss. However it depends on the type of diode and on the type of rectifier (look up half wave, full wave, bridge rectifiers, center taped, etc..)
Wall outlets are AC. They are stepped down using transformers. That way they can be sent in the power lines with high voltage and low current (to minimize I^2*R losses).
Most micro's do not have (or extremely minimal) reverse current protection.
Power electronics get very hot!!! Check the component power ratings, also you can put a heat sink on it to minimize thermal issues (even thou it will still probably be hot).