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It is not likely to bloom its first year.
With proper care you should see increasing blooms next season.
The flowers are triggered in the fall as the light levels drop, not temperatures.

Here is a link with more information.
https://www.gardeningknowhow.com/ornamental/foliage/pampas-grass/growing-pampas-grass.htm

Pampas grass can be cut to a few inches above the ground in late winter, as described in this article:
https://www.gardeningknowhow.com/ornamental/foliage/pampas-grass/pruning-pampas-grass.htm

Yes, you can- ornamental grass plumes are sometimes used in flower arrangements and may be sprayed with hairspray to increase their longevity. If they're not sprayed, I'm not sure how long they'd last, but probably until the plume dries out and disintegrates.

You can see some die back from the grass if it is not pruned.
It can also become invasive if left to reseed on it's own.
I do know several gardeners that only prune back the Pampas Grass every other year with great success.

Here is a link with more information.

You can trim your pampas grass at any time and it won't hurt the plant- any grass can be cut down by about 1/3 of its height at any time during its growing season. However, it won't flower if you cut it before flowering. You'll have to choose which is more important to you- the flower plumes or having a more manageable height.

If most of the seeds have not germinated, there may be a problem with the seeds themselves. You may want to try a germination test in seed starting mix or on a moistened paper towel indoors, and if most of the seeds don't grown, get more seeds from a different source.

Or, if the seeds have germinated but the seedlings are growing very slowly, it's possible that there is salt or a toxin in the soil that inhibits growth, or something else wrong with the conditions. Was another plant grown successfully in the same spot previously?