Prevent the word "Question" from appearing before every question?

In the subject, you can redefine the command \AMCbeginQuestion, which is originally

\def\AMCbeginQuestion#1#2{\par\noindent{\bf Question #1} #2\hspace*{1em}}

with something like

\def\AMCbeginQuestion#1#2{\par\noindent #2\hspace*{1em}}

In the separate answer sheet, you can redefine the command \AMCformQuestion, which is originally

\def\AMCformQuestion#1{\vspace{\AMCformVSpace}\par{\bf Question #1:}}

to something like

\def\AMCformQuestion#1{\vspace{\AMCformVSpace}\par{\bf #1:}}

Change the letters inside the ovals from ABCDE to FGHJK on even numbered questions?

\correctchoice{yes} can be written \correctchoice[Y]{yes} to use letter Y inside the boxes. Make your letters in an automated way should be possible, but a little tricky.

Reduce the size of the letters inside the ovals?

Again, you can use something like

\correctchoice[{\small Y}]{yes}

or even

\correctchoice[{\scriptsize Y}]{yes}

Thank you very much. It all worked!

Could you tell me please if there is any way to choose a sans serif font for the tiny type and/or to make it bold?

Still can't believe how easy it has been to get started. Thank you again.

Sans serif : \textsf{...}. Bold: \textbf{...}, as in

\correctchoice[{\small\textbf{\textsf{Y}}}]{yes}

You can also define a LaTeX command to make it more flexible:

\def\keyletter#1{{\small\textbf{\textsf{#1}}}}

(right after \begin{document}), so that you can use

\correctchoice[\keyletter{Y}]{yes}

Worked perfectly. Thank you!

you can make it easy by used \small in one time like this.

\begin{multicols}{2}\small
 .......
\end{multicols}

The following type size commands, in order of increasing font size, are supported by LaTeX.

\tiny
    \scriptsize
    \footnotesize
    \small
    \normalsize (default)
    \large
    \Large (capital "L")
    \LARGE (all caps)
    \huge
    \Huge (capital "H")

regards