cut/pull off blossom or its holder too? Or must I remove its whole stem to stimulate plant's seed production? I know it's different for taller flowers blooming on a single stem, but I mean the smaller, bushier ones, like marigolds, eg. Thanks for help!

Pluck off the ENTIRE bloom. On most plants this will encourage more blooming. On things like perennials, cut off the bloom down the stem to where the pant starts. Again, it may rebloom.

You want to use clippers and cut as close to the main stem as possible. Leaving remnants will promote mold and bacteria growth which will eventually kill the plant.
This is also true for indoor plants without blooms. All dead leaves/foliage needs to be removed from the plant and pot to discourage bacteria.
Good luck!
(*The old wives tale about promoting more flowers to grow by snapping off the dead blooms is unproven. Except after the season with the plants that hibernate for the winter. Rhododendrons, roses, lilacs, butterfly bushes will do rather well Through winter and re-blossoming for spring if you prune. But pruning is a very meticulous operation and should be researched thoroughly. Check your local garden center for a book.)