Answer if the given sentence is truly a sentence.
The dark clouds in the gloomy sky.
No
CORRECT! It does not have a verb. You could say: The dark clouds filled the gloomy sky.
Yes
Running through the woods with hearts beating through their chests.
No
CORRECT! There is no subject. You could say: I was running…
Yes
Helping others is a good way to spend your time.
Yes
CORRECT! “Helping others” is the subject. “Is a good way to spend your time” is the predicate. “Is” is the verb. 
No
The welcome mat sat proudly on the front step.
Yes
CORRECT! “The welcome mat” is the subject. “Sat” is the verb.
Photo by Don Hainzl on Pexels.com
Photo by Don Hainzl on Pexels.com
No