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If you don't want seeds, remove the blooms as they fade.

It sounds like the flower is damaged beyond repair. But, it will bloom again for you next year if you keep it.

It be very honest, it sounds like their is some sap loss from a nearby plant. There are several houseplants that have a caustic white sap that would fit the description you sent. Typically, they do not leak sap unless damaged, but if there was a pest infestation on the plant with the white sap, this could lead to dripping sap which could fall on other plants and the window sill.

I would check nearby plants for damage and see if they are dripping sap. Is there a plant that was near both the amaryllis and the orchid that may be dripping sap?

This article will help with getting them to rebloom: https://www.gardeningknowhow.com/ornamental/bulbs/amaryllis-hippeastrum/amaryllis-bloom-again.htm

It sounds like it could either be leaf galls or a fungus called red spot leaf disease. I would recommend repotting the plants (if in containers) with sterile soil and treating them with a fungicide, like neem oil.

Unfortunately, you cannot tell their color until they actually bloom. These plants, unlike many others, also bloom better when somewhat crowded. If you have had problems with your plants flowering, then your soil could be lacking phosphorus, which is responsible for blooming in plants. A soil test would confirm this. In the meantime, however, it will not hurt to add a phosphorus rich fertilizer or some bone meal to the soil where your plants are (or will be) growing.