• simply type the question code (question or questionmult environment)
• or create a group with a single element containing the question code, and insert this group…

Actually, I have a latex file with many historical questions that I have used over the past years. They are already in a group, i.e., not inserted by default in the exam.
For my new exam this year, I would like to hand-pick a few individual questions from the large file (specifying them by their name), rather than copying and pasting the code of the questions.
Is that possible? Thanks!

I don't think it is possible with LaTeX commands only.
Personally, I use a perl script to extract questions from my database (which is a simple LaTeX file with all the questions) and populate a group in a modified LaTeX source file that I can then use in AMC, so that eg.

%%Q[calculus]

\element{maingroup}{
  \begin{question}{calculus}
    ....
  \end{question}
}