Are the lens elements glued into the lens barrels?

Short answer: No

Detailed answer: You cannot glue all the lens elements to the lens tubes for several reasons:
Alignment and Orientation: Each lens element must be precisely oriented to maintain optical performance. Incorrect alignment during gluing can destroy the lens functionality.
Capillary Forces: If lens elements are too close together, capillary forces can draw glue between them, leading to optical issues.
Design Considerations: Lenses should be specifically designed for gluing, which is not the case for all lenses.
In summary, gluing lens elements can compromise optical performance and structural integrity due to alignment issues, tolerances, and design limitations.

See also:
What are the challenges in glueing lens elements into the lens barrels?