Explanation
A parameter is a global placeholder value such as a number, date, or string that can replace a constant value in a calculation, filter, or reference line.
For example, you may create a calculated field that returns True if Sales is greater than $500,000 and otherwise returns False. You can replace the constant value of "500000" in the formula with a parameter.
Then, using the parameter control, you can dynamically change the threshold in your calculation.
For example -

For Standard Deviation and Variance, we don't need to use quick table calculations, since they are available by default. See below:

However, as seen in the types of quick table calculations available in Tableau, Rank and Moving Average belong to only this category.

Explanation
Upon clicking on a filter, we see the following options:

Clearly, Regex Match is not one of these options!

Explanation
Of course! As an example, see below:
1) Using the Sample Superstore data, let's plot a bar chart showing the Sales for each Category:

Observe that we have 3 marks - Each bar in a bar chart is called a mark. Similarly, each point in a scatter plot is also a mark , and so on for all charts.
1 row by 3 columns means that clearly on the y-axis (Sales), we have only a single mark - a single continous axis, but 3 different marks (Technology, Furniture and Office supplies ) on the x-axis.
2) Now let's add subcategory to the view as well (another dimension):

Observe that the number of marks has increased - i.e the number of Bars.
Also, notice we now have 1 row and 17 columns. Simply because 1 row = Sales (on the y-axis), and on the x-axis, we have 17 different columns (i.e product sub categories!!)

Explanation
Cluster analysis partitions marks in the view into clusters, where the marks within each cluster are more similar to one another than they are to marks in other clusters.