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If they are in pots outside, they need to be watered daily and twice a day in temps over 80F. If they are in pots indoors, they need to be watered when the top of the soil is dry to the touch. If they are planted in the ground, they will need 2-4" of water a week.

They will grow new flowers next year, but likely will not regrow them this year.

You can simply snip the faded flowers off at the base of their stem.

With calla lilies, it is unlikely they will bloom again. They will likely go dormant soon so that they can build their energy for next year's blooms.

It may be too late, but you have to try. They will not survive another year in dormancy. They need to break dormancy so that they can try to store enough energy to survive another winter. You can try planting them in pots so that you can bring them in for the fall and give them a little more time to grow to store enough energy and then you can put them into dormancy again.

This sounds like a fungus is attacking the buds. You can treat the plants wil a fungicide weekly to keep the fungus away.

Calla lilies' flowers normally start out green and will gain color as the flower ages. This is normal. If the buds are not opening fully, they likely need more water. They should be watered at least daily and twice a day if the temps are over 80 F, especially if they're in containers. You can also add some phosphorus, such as bone meal, to the soil.