I have a begonia houseplant that has for some reason stopped flowering.
My bedding begonias have developed tubers. Can these be stored and will they flower next year?
This article should help: https://www.gardeningknowhow.com/ornamental/flowers/begonia/wintering-begonias-overwintering-a-begonia-in-cold-climates.htm
If I am making hanging baskets, how many begonia plants will be needed for a mid-size basket?
On average, you would put in about 3-4 plants per 10 inch basket.
My indoor pink flowering begonia has a white powdery mildew on all the leaves and has not flowered for ages. Is there a cure?
This article should help with that: https://www.gardeningknowhow.com/plant-problems/disease/powdery-mildew-homemade-and-organic-remedies.htm You can also try neem oil. In addition to being an effective organic insecticide, it's a great fungicide. Here is more information: https://www.gardeningknowhow.com/problems/pests/neem-oil-uses.htm
Need to classify large hairy leafed and stem shrub begonia for flower show. Underside of leaf is maroon with green veins, top side of leaf is medium dark green with light green veins, and flowers are pink and green for they are just starting to bloom.
Could it be begonia soli-mutata? AKA Sun Tan Begonia?
http://www.santarosagardens.com/Begonia-soli-mutata-p/beg-sol.htm
I have just found the answer to whether I can split my double begonias which have now now grown huge, but I don't have sulphur powder. Is there an alternative I can use to dust my double begonia tubers with once they have been split?
That is used as a fungicide to help ward off disease. You can also try giving them a quick did in a baking soda solution, which also acts as a fungicide:
https://www.gardeningknowhow.com/garden-how-to/info/homemade-fungicide.htm
I usually use ground cinnamon for this. Cinnamon is very anti-bacterial. I grow orchids and always dust cuts with cinnamon after dividing them,
Should the plants be cut back when they become leggy indoors in the winter? How much water do they require?
During winter months, plants need only be watered about once monthly or as needed when the soil becomes dry about an inch or so down. Leggy plants are normally a sign of too little light. You can cut them back some and begin giving the plants more light. Here is some additional information that should help: https://www.gardeningknowhow.com/ornamental/flowers/geranium/leggy-geranium.htm, https://www.gardeningknowhow.com/ornamental/flowers/begonia/wintering-begonias-overwintering-a-begonia-in-cold-climates.htm, https://www.gardeningknowhow.com/ornamental/flowers/geranium/how-to-save-geraniums-over-the-winter.htm