yes, h=1/sigma(standard deviation)
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A probability density function assigns a probability value for each point in the domain of the random variable. The probability distribution assigns the same probability to subsets of that domain.
The Gaussian probability density distribution (pdf) is referred to as the Normal distribution. The Gaussian model results in a Gaussian pdf. Interesting, it didn't come from Gauss, but de Moivre, one of the greatest mathematicians of the 18th century, at least in my opinion. See related links.
That's a Gaussian distribution.
what is density curve
Yes. When we refer to the normal distribution, we are referring to a probability distribution. When we specify the equation of a continuous distribution, such as the normal distribution, we refer to the equation as a probability density function.