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This usually depends on where you live. In northern areas, daffodil plants can usually be left alone and will return the next growing season. In southernmost regions, they are either treated as annuals or dug up and stored until the return of cooler temps.

This could be due to any number of things. If they did not have sufficient chilling, then their blooming will be poor. If the plants are overcrowded, then blooming will be decreased. Light and drainage can be issues as well, but only if nearby trees, etc. have recently changed would this affect you. Finally, the soil could be lacking phosphorus, which is important for flowering. You can mix bone meal in the soil around your plants to add more phosphorus. For additional information, this article will help: https://www.gardeningknowhow.com/ornamental/bulbs/daffodil/daffodils-not-blooming.htm

No, this shouldn't affect the daffodil bulbs as long as you're careful not to overwater the area, which could lead to the bulbs rotting. Also, you would have to be careful when harvesting your shallots so as not to disturb the dormant daffodil bulbs.

While you can plant them in the ground now, you may want to wait for fall so the bulbs go through their natual cooling period. These articles should help: https://www.gardeningknowhow.com/ornamental/bulbs/daffodil/daffodil-planting-care-tips-how-to-plant-daffodils-in-your-garden.htm, https://www.gardeningknowhow.com/ornamental/bulbs/bgen/how-to-plant-a-flower-bulb-in-your-garden-after-winter-forcing.htm

As long as they were planted in a suitable location with adequate drainage, they should be fine. They will continue to fade and go dormant but should return next year.

If the bulbs are pre-chilled, they take about 6-8 weeks to grow and bloom. If they are not pre-chilled, you will need to chill them for 6-12 weeks and then plant them (and wait 6-8 weeks for them to bloom).