Can an object be moving for 10 seconds and still have zero displacement?

Very easily.

Displacement is the distance between where you start and
where you end.  The route you take to get there doesn't matter.

Here are three ways to move for 10 seconds and wind up
with zero displacement:

-- Walk away from a tree for 5 seconds, then turn around,
and walk back to the tree in the next 5 seconds.

-- Walk all the way around the tree in 10 seconds, back to
where you started.

-- Go inside and stand at the bottom of the steps.
Step up on the first step, then step back down from it.
Keep doing this for 10 seconds.

The answer is 12, for the points