We live in Rhode Island and our potted Hibiscus plant is several years old. We take it inside in early fall and out again in late spring. When should we prune the plant? It gets very leggy this time of year. Also, we don't get many blooms in the summer. What should we do to promote blooms? Finally, where should we keep the plant during the winter months? Does it need sunlight in the winter and only light watering?
First, winterizing the hibiscus requires some light and a bit of watering, but generally not a lot of either. https://www.gardeningknowhow.com/ornamental/flowers/hibiscus/wintering-hibiscus-indoors-winter-care-for-hibiscus.htm
As to pruning the plant, this link will take you to an informative article: https://www.gardeningknowhow.com/ornamental/flowers/hibiscus/tips-for-pruning-hibiscus-plants-when-to-prune-hibiscus.htm
To encourage blooms, you may want to fertilize your plant, and here's an article about that:
https://www.gardeningknowhow.com/ornamental/flowers/hibiscus/hibiscus-fertilizing.htm
There is a hibiscus growing in the basement window well of the house I just moved into. Looks like it has been there for a few years. About five feet tall. Or can I take a cutting and restart? How would I do that?
You can do either, but it looks like a Rose of Sharon to me by the foliage. It looks like you have a maple tree as well.
You can try digging up the shrub and immediately transfer it into a container, with as much of the rootball intact as possible. Keep it watered well till it revives after transplant shock. They get 8 to 10 feet tall if you'd rather plant it in the ground.
https://www.gardeningknowhow.com/ornamental/shrubs/rose-of-sharon/rose-of-sharon-plant-cuttings.htm
I bring it inside in the winter but not sure what to do with it once inside. Last year it dropped all its leaves but after a couple of months it started to look better and produce leaves.
Hibiscus will go through a semi-dormant state indoors. What you have witnessed in the past is considered normal behavior for the plant.
The most important thing will be to leave it alone until Spring. At that time, you can trim it back and prepare it for the growing season.
Here are some articles that will help:
https://www.gardeningknowhow.com/ornamental/flowers/hibiscus/how-to-care-for-hibiscus-plants.htm
My hibiscus hasn’t flowered at all this year. I let it winter in my garage last year, then brought it back outside in the spring. It had grown to a height of over 7 feet, but no blooms!
You may need to add some phosphorous to your plant's soil
Here's an article with tips on how to fertilize your hibiscus:
https://www.gardeningknowhow.com/ornamental/flowers/hibiscus/hibiscus-fertilizing.htm
This is the 3rd year for this bush
Yes, but wait till they are dormant in late winter or early spring.
https://www.gardeningknowhow.com/ornamental/flowers/hibiscus/pruning-perennial-hibiscus.htm
What should I do to prepare perennial hibiscus seeds for spring planting?
It's important to remember that the seeds need to stay dry, so whether you put them in a brown paper bag or freeze them for the winter, make sure they don't get warm or wet. Here are three articles with different tips about how to preserve your seeds for spring planting:
https://www.gardeningknowhow.com/ornamental/flowers/fgen/harvesting-garden-seeds.htm
https://www.gardeningknowhow.com/garden-how-to/propagation/seeds/storing-seeds.htm
https://www.gardeningknowhow.com/garden-how-to/propagation/seeds/does-freezing-kill-seeds.htm
I have two hibiscus plants in pots. One has done reasonably well over the summer, the other has barely survived. They both now have yellow leaves and the poorer one is losing them. They are both however producing ne growth, how can I ensure they they flourish better?
Hibiscus require, near constant, feeding in container. This will be the primary reason for leaf drop. They won't tolerate being overwatered, either. Have care to let them dry out, thoroughly, down to about 2 or 3 inches between watering.
Here are some articles that will help:
https://www.gardeningknowhow.com/ornamental/flowers/hibiscus/hibiscus-container-care.htm
https://www.gardeningknowhow.com/ornamental/flowers/hibiscus/hibiscus-fertilizing.htm