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Yes, you can cut the flower stalks to the base of the plant now or fall. It won't hurt either way. In fact, you can even leave them for fall or winter interest if desired.

No, these plants do not require deadheading and the spent blooms actually add interest to the fall/winter garden. You can, however, opt to cut back the entire flower stalk once it's turned brown.

Some varieties are hardy to zone 3.
If your unsure of the variety you bought, mulching them will help.
I garden in zone 4 and my Liatris winter over in a slightly protected area.
Here is a link with more information.

https://www.gardeningknowhow.com/ornamental/flowers/liatris/liatris-blazing-star.htm

Yes, you can start your plants indoors in pots, then move outdoors after danger of frost.
I like to place 3 or 4 corms in a 8 to 10" pot with good potting mix.
Water them and place them in a bright and cool location.

https://www.gardeningknowhow.com/ornamental/flowers/liatris/liatris-blazing-star.htm

Liatris are winter hardy in zones 5 and above. If this is where you are, they will probably be fine outside.

In colder zones (and possibly in the colder portions of their range, since container plants are more exposed to cold than those in the ground) you will need to dig up the underground corms for storage indoors. Pack them in moistened peat moss and store in a cold but not frozen location, such as the refrigerator or unheated basement.

https://www.gardeningknowhow.com/ornamental/flowers/liatris/liatris-blazing-star.htm

Yes, you should dead head your Liatris perennial plant.
When the flowers fade you can use a garden shear to cut the spent flower down to the base of the plant.
This serves to tidy up the plant but can also stimulate additional flowering.

Fertilizing right after pruning with a 'bloom stimulator' fertilizer can actually give you another round of flowers.
Cut the application rate in half and water afterwards to avoid burning the roots.

Cut all spent flowers to the top of the foliage in the fall.