I planted a mum in my flower bed this summer after planting it I see the tag said it was hardy to 32 degree should I dig it up I am in zone 5b can I put mulch around it an cover it will it be ok to leave it in the ground this winter?
Has it bloomed? If the tag says it's only hardy to 32 degrees, I wouldn't expect it to return next year, even with mulch. If it has already bloomed and you've enjoyed it, you could try to winterize it, but don't be disheartened if it doesn't return. Even the ones that are hardy often don't return. (If you want to keep it, you can bring it inside for the winter or in the garage, above 32 degrees F, and water occasionally.)
https://www.gardeningknowhow.com/ornamental/flowers/chrysanthemum/wintering-mums.htm
Just blooming for first time now! Is it a genuine winter bloomer? Do I leave it to the frosts?
It is a beautiful garden chrysanthemum. They are fall perennials and withstand a few light frosts.
https://www.gardeningknowhow.com/ornamental/flowers/chrysanthemum/growing-chrysanthemum-flowers.htm
What the type of these flowers??
That appears to be one of many Chrysanthemum- Probably Chrysanthemum indicum.
Here are a couple of articles that will help:
https://www.gardeningknowhow.com/ornamental/flowers/chrysanthemum/annual-vs-perennial-mums.htm
https://www.gardeningknowhow.com/ornamental/flowers/chrysanthemum/growing-chrysanthemum-flowers.htm
Mums are head-drooping. No new blooms.
It depends on the species. Most are annual, and will die off after flowering for the year. If you do have a perennial type, then pruning and feeding may be in order. This article will offer more information:
https://www.gardeningknowhow.com/ornamental/flowers/chrysanthemum/chrysanthemum-lifespan.htm
In additional to play with wet-dry soil can I use something else to help my chrysanthemum? Can I use Neem Oil on foliage?, or Trichoderma for soil?
Unfortunately, your photos did not come through. I am unable to see the issue. The correct actions to take will depend on what is causing the wilting. If this is fungal, or bacterial, in nature then fungicides will be the option. If this is from over, or underwatering, then correcting watering habits will be necessary.
Since most of the Trichoderma species found in soil are, also, found in ambient air, chances are that it is already present in the soil. Adding any more will only be beneficial to an otherwise healthy plant.
In the meantime, here are some articles that will help:
https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/testing-moisture-in-plants.htm
https://www.gardeningknowhow.com/ornamental/flowers/chrysanthemum/growing-chrysanthemum-flowers.htm
Where can I get chrysanthemum starts at this time of the year? I've been to five stores and none of them carry them. I'd prefer organic. Thanks!
I would check with online nurseries. Also check with friends or neighbors who have mums and might let you take cuttings.
do they have bulbs that have to be dug up in winter or do they come back in bloom when spring
Partly. Pyrethrins in the Chrysanthemum are a spot killer. They don't do much once dry, though, except for pests that ingest it.
Here is an article to help:
https://www.gardeningknowhow.com/ornamental/flowers/chrysanthemum/chrysanthemum-pest-control.htm
https://www.gardeningknowhow.com/plant-problems/pests/insects/mosquito-repelling-plants.htm
https://www.gardeningknowhow.com/ornamental/flowers/chrysanthemum/growing-chrysanthemum-flowers.htm