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I think that you should store them away until Fall! The heat will not allow for a proper transplant.

https://www.gardeningknowhow.com/ornamental/bulbs/lily/oriental-lily-plant-care.htm

Wild daylilies will transplant quite well, but this time is not appropriate. Any other time of year will be fine, but this hot portion of the year can lead to a failed transplant. That isn't to say that you can't try it, but it does tend to lead to a higher failure rate in summer. However, after the final bloom of the summer, it will begin to slow down and focus on root growth. This will guarantee a successful transplant.

Keep in mind that these orange ditch lilies are very invasive. You may want to keep these in container to keep them from taking over the area that you want them in.

https://www.gardeningknowhow.com/ornamental/bulbs/daylily/how-to-transplant-daylilies.htm

https://www.gardeningknowhow.com/ornamental/bulbs/daylily/controlling-daylilies.htm

Sure! But their care depends on their types. Unfortunately, your photos did not come through, so I am unable to see what you have.

https://www.gardeningknowhow.com/ornamental/bulbs/bgen/transplanting-bulbs-in-gardens.htm

These two publications say the same thing. Although the bulb has a somewhat long neck, the plump part of the bulb should be planted 3 to 4 inches deep. I think it is less important that the top of the bulb be above soil, because that was not a common instruction.

https://hort.extension.wisc.edu/articles/aztec-lily-sprekelia-formosissima/

https://www.ocregister.com/2017/12/11/master-gardener-how-to-grow-aztec-lillies/

No you wouldn't cut them back before the bloom because you might cut off the developing flowers. Afterwards, the lily needs all its leaves to gather energy to store in the bulb for next year. You can stake them or grow them in tomato-like cages if they don't stand on their own. Once the foliage dies back, you can cut the stem to the ground.

For those plants, you could get away with fluorescent lights, or LED. There are some horticultural LEDs on the market that will fit a standard base, but are more suited for plants than a standard bulb.

Otherwise, there are numerous plant fixtures on the market that will suit your purpose. Generally, you are going to opt for around 70 to 100 watts per square foot of growing space, but you could far exceed that for optimum growth.

https://www.gardeningknowhow.com/houseplants/hpgen/fluorescent-lighting-for-indoor-gardening.htm

https://blog.gardeningknowhow.com/trends/top-5-benefits-of-led-grow-lights/