When and how is the best time to prune brooms?
This article should help you prune your broom plants:
https://www.gardeningknowhow.com/ornamental/shrubs/broom-plants/scotch-broom-pruning.htm
I want a liwuod solution high on Phosphorus that I can spray on this stuff with my tank sprayer and kill it or at least thin it out. I have 5 acres of it that I want to kill, but I want to keep my grass. Is there a product I can buy or can I make a home remedy to do the job.
Herbicides do not work well on Broom Sage.
These links have more information.
https://extension.tennessee.edu/Smith/Pages/anr-What-do-I-do-about-broomsedge.aspx
https://www.gardeningknowhow.com/plant-problems/weeds/broomsedge-grass.htm
I would also suggest you talk with your County Extension Office. They may have some suggestions for control of Broom Sage, specific to your region.
My broom shrub is getting fairly tall. I would like to cut it back, but don't know if I should.
You can do some hard pruning, but this will have to be done in late spring only. This article will give you more information: https://www.gardeningknowhow.com/ornamental/shrubs/broom-plants/scotch-broom-pruning.htm
My broom plants have lost all flowers and most leaves after just 3 weeks. Why? Can't see any pests on them.
Without pictures and a detailed description of its care, the temperature and watering habits, and the area that it is planted, it would be very difficult to give you any useful diagnosis without guessing. It could be a great number of issues.
Please include photos and the details listed above and I will be more than glad to help.
In the meantime, this article will give you information on th care of these: https://www.gardeningknowhow.com/ornamental/shrubs/broom-plants/how-to-plant-broom-shrubs.htm
Does this broom need trimming?
This article will help you with pruning.
https://www.gardeningknowhow.com/ornamental/shrubs/broom-plants/scotch-broom-pruning.htm
I can find tons of info about broom plants, but all of it ignores a fundamental question: When planting broom seeds, how far apart should they be spaced? Maybe this info is available somewhere, but I can't find it. Any suggestions?
It is widely recommended to space them at least 4 feet apart, but up to 10, depending on cultivar. They are quite invasive in most areas and will self spread becoming one large clump over time.
https://www.gardeningknowhow.com/ornamental/shrubs/broom-plants/information-on-broom-shrubs.htm
Canada, zone 4a, hardiness 40.
Broom plants are hardy to zone 5, so yes, you would need to overwinter it indoors to keep it sheltered till spring. I would plant it in soil, though, and not keep it in water all winter. Keep it in a sunny spot free of drafts from the furnace.
These articles should help:
https://www.gardeningknowhow.com/ornamental/shrubs/broom-plants/how-to-plant-broom-shrubs.htm
https://www.gardeningknowhow.com/garden-how-to/info/what-is-overwintering.htm