Is there a single word or expression for all the tests/checks done before doing the actual task? The context is to describe the tests that are performed to check the safety and other operational issues of the system before the actual testing.
"Pilot or Pilot Test" could be a candidate. Pilot means:
Something serving as a test or trial.
Pilot test, pilot study, pilot project, pilot experiment are used broadly.
A test name could differ depending on each industry, and alpha/beta tests are also braodly used in many industries such as gaming industry as Joe Dark suggested in the comment. All of them could be called a "preliminary" test.
something that comes first in order to prepare for or introduce the main part of something else.
Consider smoke testing or smoke test:
Smoke testing is non-exhaustive software testing, ascertaining that the most crucial functions of a program work, but not bothering with finer details.
Another word would be sanity testing or confidence testing (source).
This may be industry-dependent, but that's what we call basic daily sanity tests in the software/tech field. More in-depth testing is typically required later on.