Sure! This can be done quite easily. These articles will help:
https://www.gardeningknowhow.com/ornamental/trees/silk-floss/floss-silk-tree-planting.htm
https://www.gardeningknowhow.com/ornamental/trees/kapok/kapok-tree-pruning.htm
flower and is there a soil amendment that I should add? I am a California Master Gardener. Thanks for your help.
Yes, they are very prolific bloomers! Your issue could be an indication that the nutrition ratios in your soil could be a bit off, namely low in phosphorus and potassium and high in nitrogen.
It could also indicate a low pH, or acidic soil.
I would recommend testing your EC and nutrient profile, as well as pH. Then amend accordingly.
These links will help:
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/testing-soil.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/soil-ph-plants.htm
https://www.gardeningknowhow.com/ornamental/trees/silk-floss/floss-silk-tree-planting.htm
https://www.gardeningknowhow.com/ornamental/trees/kapok/kapok-tree-pruning.htm
My young silk floss tree has not fared well this winter. İt was planted 3 years ago)but this winter was colder and the branches from the top have darkened down the tree to about a third down. New shoots have just started to sprout below this for about a foot. İ think the top part of the tree is dead but don't know whether to cut off the branches above the new growth or leave them.
Yes, you can cut them back to a good bud or a lateral branch. Do not leave a stub.
https://www.extension.purdue.edu/extmedia/HO/HO-4-W.pdf
https://www.gardeningknowhow.com/ornamental/trees/silk-floss/floss-silk-tree-planting.htm
Can I root the broken limb and do I need to do anything to the top that is still in the soil?
I would try to root the cutting. Hopefully, since your tree is small, topping it will encourage branching. You don't need to do anything to the remaining stalk.
Here is information on rooting cuttings and taking care of a floss silk tree.
https://www.gardeningknowhow.com/ornamental/trees/silk-floss/floss-silk-tree-planting.htm
https://www.gardeningknowhow.com/ornamental/trees/tgen/planting-trees-from-twigs.htm
Last year I bought 3 young Floss Silk Trees. nOW THEY ARE ABOUT 1,5m high. Everything is fine for the two of them but all the new leaves of the third one are getting black immediately and fall. Can you help me?
Unfortunately, your photos did not come through. I am unable to see the damage. There are several infections that can plague the tree. These articles will help:
https://www.gardeningknowhow.com/ornamental/trees/mimosa/growing-silk-trees.htm
https://www.gardeningknowhow.com/ornamental/trees/mimosa
https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm