Yes, a trellis is necessary to support luffa gourd plants.
Luffa gourds are prolific growers with an abundance of vines and will need sturdy trellises as they grow and mature. Keeping the vines off the ground allows the gourds to grow straighter, and also prevents rot and disease.

Yes, luffa gourds are edible when harvested young.
Early green luffa gourds are a great summer fruit. It can be harvested and eaten similarly to zucchini or squash. Luffa gourd has a small window for use as fruit. As it matures, its center becomes fibrous and not suited for eating. Its mild and sweet flavor makes luffa gourd great sliced, grilled, and sauteed, or in soup, curry and salads.

Let your luffa gourd mature on the vine until their skin turns to a yellow-brown color. Peel the gourd, then rinse it with water and squeeze to remove all the seeds and flesh. Allow your luffa to completely dry and cut them into usable sizes.

Select a fully mature and dried luffa gourd. Peel the gourd and remove the skin. The black seeds should fall out easily. Spread out these seeds and allow them to fully dry. Once dry these seeds can be stored in a cool, dry location to be planted during another season.