Why when flowers start to open they just laid flat
This article goes over the reasons an agapanthus might not bloom, and it should help you pinpoint your problem:
https://www.gardeningknowhow.com/ornamental/bulbs/agapanthus/agapanthus-not-flowering.htm
Is it all right to actually pull the whole dead stalk out of the plant, once it has flowered?
I would recommend cutting the stalk as close to the base as possible. Pulling the entire stalk may cause damage to the roots. Here is some more information: https://www.gardeningknowhow.com/ornamental/bulbs/agapanthus/cutting-back-agapanthus.htm
When should I bring my pots of agapanthus into the shed for winter? Before or after the first frost? Also should I keep them watered during their "holiday" in the shed?
These plants are hardy down to about 20 degrees or so. Frost will not harm them, however when the temperatures drop close to unsafe levels, it would be best to bring them in. It is always good to reduce watering when over wintering, so that you do not get a fungus. Here is an article on their care: https://www.gardeningknowhow.com/ornamental/bulbs/agapanthus/agapanthus-plant-care.htm
I grow my Agapanthus plants in pots and overwinter them in an unheated greenhouse. What are the important points to carry out?
There isn't much to be done about caring for these in container. It should survive just fine in greenhouse without much help. It is worth noting that this plant is toxic and irritant to skin, so be very cautious when handling this plant.
This article will give you more information on the care of Agapanthus:https://www.gardeningknowhow.com/ornamental/bulbs/agapanthus/agapanthus-plant-care.htm
My lilies of the Nile have been planted for years. I live in North Florida. When we have a cold winter, I just cut them back and they come out again. There are some exposed dangling roots. Should I cover these with more dirt? Also, they don't bloom much. What can I do to make them bloom more? They are in a part sun area. We have a sprinkler system and sandy soil. They get watered everyday in the summer.
You will want to put a layer of compost and mulch over these once every year or every two years. This will replenish the nutrients in the soil, as this is what is likely causing them to not flower. It will also help with the aerial roots. This article will help you: https://www.gardeningknowhow.com/ornamental/bulbs/agapanthus/agapanthus-plant-care.htm
My evergreen agapanthus are looking crumpled and yellow after the snow smothered them. What should I do to revive them please?
Wait until it is warmer, and new growth returns, and you can prune off anything that dies after this time. It will likely recover. Just care for it as usual. This article will give you more information on the care of these: https://www.gardeningknowhow.com/ornamental/bulbs/agapanthus/agapanthus-plant-care.htm
Several of my blue agapanthus plants have flowers popping out in the middle of the stem and a full bloom on the top. What causes this?
This is a naturally occurring event and nothing to be concerned about.
https://www.gardeningknowhow.com/ornamental/bulbs/agapanthus/agapanthus-plant-care.htm