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These are highly invasive trees in most areas. These will be very hard to get rid of. This article will help: https://www.gardeningknowhow.com/ornamental/trees/tgen/kill-zombie-tree-stump.htm

It can take a few years before mimosa/silktree starts blooming, but at 8 feet and 3 years you may not be far off now.

https://www.gardeningknowhow.com/ornamental/trees/mimosa/growing-silk-trees.htm

There is no reason to remove the seed pods from the mimosa trees except aesthetics or to prevent unwanted reseeding. If you don't like the look or the litter, go ahead and trim them off if you can reach them. If you let them fully mature and fall to the ground, you can sweep, rake or pick them up if needed. The second article discusses the problems of reseeding.

https://www.gardeningknowhow.com/ornamental/trees/mimosa/growing-silk-trees.htm

https://www.gardeningknowhow.com/ornamental/trees/mimosa/mimosa-tree-weeds.htm

Try digging up a few of the saplings, by digging out around them about a foot in diameter from the base. Get off what dirt you can very carefully, salvaging as many smaller roots as possible. Try not to break them at this point, but you won't be able to avoid it completely. Put them into a container, and bring them inside under lighting, or in a bright window. Treat it as a houseplant until it perks up, just to make sure that it didn't die from transplant. Once it shows signs, then you can look into shipping since it will be in a light potting mix, and you will know for sure that it is alive.

Unfortunately, that's not going to work with this type of plant. Flower color change can only occur if the genes for it are there. This is quite rare in plants. It will work with your Hydrangeas but not for Mimosa.

You, simply, have a white or light flowering variety.

Here is an article to help you with the care of the tree:

https://www.gardeningknowhow.com/ornamental/trees/mimosa/growing-silk-trees.htm

Yes, this can be normal. These short lived trees only live for one or two decades before dwindling out. Enjoy what it does produce until its demise.

It's one of those trees that you hate it or love it. Many people have fond memories of the tree during their childhood. Unfortunately, it produces a bounty of seeds that come up anywhere and everywhere. And the tree can suddenly die on you with no apparent reason. Plus it is pest prone. Most tree professionals advise against planting it. So if yours is on the way out, you might consider something else as its replacement.