Please see attached photos. We planted Gayfeather (Liatris Spicata) for the first time. After a hot spell, some of the flower stalks appear to show flowers that were going to open but dried before they had a chance - I'm pretty sure those flowers won't bloom. In the photos those flowers that were about to open appear beige-brown. Do I cut those sections off? Do I cut off the plant right below these?

You can cut the stem anywhere that suits you as long as you leave the leaves. Liatris dies back to the ground in the fall and re-emerges in the spring to start a new season.

When the flower bearing stalk is 95% dead, I cut it back to a point 2-3" below that. They typically branch for me at the leaf junction just down the stem from there.
It seems to take about 4 weeks before those side bloom stalks flower. They typically have less flowers.

Thank you. Where a stalk is bright pink at the bottom with blooming flowers, but with dried flower buds above, should I cut right above the pink, OR, cut the whole flower stalk below the pink blooms? We'd hate to get rid of the colorful bloom parts at the bottoms of the affected flower stalks if we don't have to. Also, do you think heat caused those flower beds not to continue developing, or could it have been overwatering? (we were watering them in the pot daily until we planted them so they wouldn't dry out from sun while in the pot).

They do produce a few buds down there but it is your judgement call. When the inflorescence is 90+% done, brown, then I cut them.
Just don't cut them too far down the stem.

Liatris blooms from the top down rather than from the bottom up so perhaps your tops had bloomed and you missed it? Sometimes I cut mine, sometimes I just leave the stalks for winter interest. The heat probably shortens the bloom time I would guess.

DebbieC, ahhhhh, that explains it. I thought it bloomed from the bottom up. If a flower stalk is 85-90% done, and we cut it right below the stock, is there any chance it will bloom again before frost?

I'm not sure; my season is much shorter so I haven't experienced that but why don't you give it a try and see?